Tootfinder

Interesting graph from @….
There was a •fascinating• 99pi about the push to create an official Category 6 — and the surprisingly compelling arguments against doing that (more fully developed in the story audio than in the web text summary):
https://99percentinvisible.org/episode/category-6/
One thing that’s a clear point of consensus in that debate is that the existing Saffir-Simpson hurricane scale isn’t up to the task of describing what we face now. https://fediscience.org/@rahmstorf/115481161250561175

Category-Aware 3D Object Composition with Disentangled Texture and Shape Multi-view Diffusion
Zeren Xiong, Zikun Chen, Zedong Zhang, Xiang Li, Ying Tai, Jian Yang, Jun Li
https://arxiv.org/abs/2509.02357

Category-Aware 3D Object Composition with Disentangled Texture and Shape Multi-view Diffusion
In this paper, we tackle a new task of 3D object synthesis, where a 3D model is composited with another object category to create a novel 3D model. However, most existing text/image/3D-to-3D methods struggle to effectively integrate multiple content sources, often resulting in inconsistent textures and inaccurate shapes. To overcome these challenges, we propose a straightforward yet powerful approach, category+3D-to-3D (C33D), for generating novel and structurally coherent 3D models. Our method…

The singularity category as a stable module category
Xiao-Wu Chen, Zhengfang Wang
https://arxiv.org/abs/2509.01056 https://arxiv.org/pdf/2509.01056

The singularity category as a stable module category
We investigate the stabilization $\mathcal{S}$ of the module category over an artinian ring $Λ$ by formally inverting the tensor endofunctor given by the bimodule of relative noncommutative differential $1$-forms. It turns out that $\mathcal{S}$ is a Frobenius abelian category, which is equivalent to the category of finitely presented modules over the zeroth component $L_0$ of the Leavitt ring $L$. It follows that $L_0$ is an FC ring in the sense of Damiano, which is usually not quasi-Frobeniu…

Cohomology of Small Cartesian Closed Categories
Mirai Ikebuchi
https://arxiv.org/abs/2510.00488 https://arxiv.org/pdf/2510.00488

Cohomology of Small Cartesian Closed Categories
We show the isomorphism between the Quillen cohomology and the Baues-Wirsching cohomology of a cartesian closed category (CCC). This is an extension of the results of Dwyer-Kan for small categories and Jibladze-Pirashvili for small categories with finite products. These results implies that The Quillen cohomology of a CCC C coincides with that of C as a category with finite products, and also that of C as a small category

Hurricane Melissa hit Jamaica as category 5 storm
It dropped to a category 4 cyclone as it exited the island
https://www.theguardian.com/world/live/2025/oct/28/hurricane-melissa-live-u…

CMRAG: Co-modality-based document retrieval and visual question answering
Wang Chen, Guanqiang Qi, Weikang Li, Yang Li
https://arxiv.org/abs/2509.02123 https://

CMRAG: Co-modality-based document retrieval and visual question answering
Retrieval-Augmented Generation (RAG) has become a core paradigm in document question answering tasks. However, existing methods have limitations when dealing with multimodal documents: one category of methods relies on layout analysis and text extraction, which can only utilize explicit text information and struggle to capture images or unstructured content; the other category treats document segmentation as visual input and directly passes it to visual language models (VLMs) for processing, ye…

Interview with Lovable CEO Anton Osika on competition, staying in Europe, and more; the company now has 2.3M active users, including 180K paying subscribers (Dominic-Madori Davis/TechCrunch)
https://techcrunch.com/2025/09/01/lovables-ceo-is…

Lovable's CEO isn't too worried about the vibe-coding competition | TechCrunch
Lovable specializes in helping people build apps and websites, especially people with no coding experience. It's one of the standouts in the popular AI category known as vibe-coding, which lets users guide AI models as they produce code, websites, or whole applications.

arxiv_collab: Scientific collaborations in physics (1995-2005)
Collaboration graphs for scientists, extracted from the Los Alamos e-Print arXiv (physics), for 1995-1999 for three categories, and additionally for 1995-2003 and 1995-2005 for one category. For copyright reasons, the MEDLINE (biomedical research) and NCSTRL (computer science) collaboration graphs from this paper are not publicly available.
This network has 31163 nodes and 120029 edges.
Tags: Social, Collaborati…

Comparing dg category models for path spaces via $A_\infty$-functors
Manuel Rivera, Yi Wang
https://arxiv.org/abs/2510.01080 https://arxiv.org/pdf/2510.010…

Comparing dg category models for path spaces via $A_\infty$-functors
We construct a many-object dual version of Chen's iterated integral map. For any topological space X, the construction takes the form of an A-infinity functor between two dg categories whose objects are the points of X: the domain has as morphisms the singular (cubical) chains on the space of (Moore) paths in X and the codomain has morphisms arising by totalizing a cosimplicial chain complex determined by the dg coalgebra of singular (simplicial) chains in X. When X is simply connected, we show…

Motivic homotopy theory for perfect schemes
Christian Dahlhausen, Jeroen Hekking, Storm Wolters
https://arxiv.org/abs/2510.01390 https://arxiv.org/pdf/2510…

Motivic homotopy theory for perfect schemes
We construct a perfect version of Morel--Voevodsky's motivic homotopy category over a perfect base scheme in positive characteristic. By checking the axioms of a coefficient system, we establish a six-functor formalism. We show that multiplication by $p$ is already invertible in the perfect motivic homotopy catgory. By work of Elmanto--Khan the functor sending an $\mathbb{F}_p$-scheme $S$ to the category $\mathrm{S}\mathcal{H}(S)[1/p]$ is invariant under universal homeomorphisms, hence under pe…

The ribbon category of representations of a crossed module
Ony Aubril
https://arxiv.org/abs/2510.01809 https://arxiv.org/pdf/2510.01809

The ribbon category of representations of a crossed module
The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of crossed module of finite groups. Here we study how to extend the construction of the Drinfeld quantum double for any other kind of crossed module of finite groups. This leads to a Hopf algebra D(G, H) that presents similarities with a Drinfeld double. We then s…

Notions of Cauchy completeness for normed categories
Dirk Hofmann, Walter Tholen
https://arxiv.org/abs/2510.00912 https://arxiv.org/pdf/2510.00912

Notions of Cauchy completeness for normed categories
As already mentioned by Lawvere in his 1973 paper, the characterisation of Cauchy completeness of metric spaces in terms of representability of adjoint distributors amounts to the idempotent-split property of an ordinary category when the governing symmetric monoidal-closed category is changed from the extended real half-line to the category of sets. In this paper, for any commutative quantale \(\mathcal{V}\), we extend these two characterisations of Lawvere-style completeness to \(\mathcal{V}\…

Monoid Structures on Indexed Containers
Michele De Pascalis, Tarmo Uustalu, Niccol\`o Veltr\`i
https://arxiv.org/abs/2509.25879 https://arxiv.org/pdf/2509.…

Monoid Structures on Indexed Containers
Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the scope of dependently typed programming. When interpreting types to be sets, a container describes an endofunctor on the category of sets while an I-indexed container describes an endofunctor on the category Set^I of I-indexed families of sets. We consider the monoidal structure on the category of I-indexed containe…

Hurricane #Melissa is the third Category 5 storm of the 2025 Atlantic season. This is only the second time that's ever happened.

Hurricane Melissa Makes 2025 Only Second Season with More Than Two Category 5 Storms
This is only the second time we’ve had more than two Category 5 storms in a single Atlantic hurricane season

Just finished "Thief of the Heights" written by Son M. and illustrated by Robin Yao. It's a very cool graphic novel about the illusions of meritocracy and loyalty to one's roots, with an interesting setting and better politics than most stuff out there, even if the plotting is a little rough and perhaps a bit too straightforward. The neat ending and reliance on heroism are themes I don't love in these kinds of tales, but I'm grateful for more stories in this category to exist in the first place, so I can't complain too much.
It's got disability, queer, and POC representation and some of that is #OwnVoices, which is cool, although those dimensions of the work aren't its focus.
#AmReading

On generalized morphisms associated to endofunctors of C*-algebras
Georgii S. Makeev
https://arxiv.org/abs/2509.02001 https://arxiv.org/pdf/2509.02001

On generalized morphisms associated to endofunctors of C*-algebras
We introduce a class of good endofunctors of $C^{*}$-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of $C^{*}$-algebras and a good endofunctor, we construct a commutative monoid of generalized morphisms, and endow these monoids with a bilinear composition. This construction generalizes the homotopy category of asymptotic homomorphisms used in the definition of the Connes-Higson $E$-theory. …

RB Craig, QB Anderson advance in HOF process https://www.espn.com/nfl/story/_/id/46465226/roger-craig-ken-anderson-advance-hof-senior-nominees

MMDEW: Multipurpose Multiclass Density Estimation in the Wild
Villanelle O'Reilly, Jonathan Cox, Georgios Leontidis, Marc Hanheide, Petra Bosilj, James Brown
https://arxiv.org/abs/2510.02213

MMDEW: Multipurpose Multiclass Density Estimation in the Wild
Density map estimation can be used to estimate object counts in dense and occluded scenes where discrete counting-by-detection methods fail. We propose a multicategory counting framework that leverages a Twins pyramid vision-transformer backbone and a specialised multi-class counting head built on a state-of-the-art multiscale decoding approach. A two-task design adds a segmentation-based Category Focus Module, suppressing inter-category cross-talk at training time. Training and evaluation on t…

Accepting Normalization via Markov Magmoids
Elena Di Lavore, Mario Rom\'an
https://arxiv.org/abs/2510.01131 https://arxiv.org/pdf/2510.01131

Accepting Normalization via Markov Magmoids
Normalization of probability distributions is not a distributive law. We introduce distributive sesquilaws to abstract normalization and, from their axioms, we derive some of its properties. In particular, normalized channels form a unital magmoid with an action of the category of subdistributions; its possibilistic analogue is the action from may-must relations into the category of relations. We argue that the magmoid of normalized channels is the stochastic analog of the category of relations.

Hurricane Humberto grows to Category 5, could affect East Coast – NBC Los Angeles
https://www.nbclosangeles.com/news/national-international/hurricane-humberto-category-5-east-coast/3783900/

CreAgentive: An Agent Workflow Driven Multi-Category Creative Generation Engine
Yuyang Cheng, Linyue Cai, Changwei Peng, Yumiao Xu, Rongfang Bie, Yong Zhao
https://arxiv.org/abs/2509.26461

CreAgentive: An Agent Workflow Driven Multi-Category Creative Generation Engine
We present CreAgentive, an agent workflow driven multi-category creative generation engine that addresses four key limitations of contemporary large language models in writing stories, drama and other categories of creatives: restricted genre diversity, insufficient output length, weak narrative coherence, and inability to enforce complex structural constructs. At its core, CreAgentive employs a Story Prototype, which is a genre-agnostic, knowledge graph-based narrative representation that deco…

Unital Specker $\ell$-groups and boolean multispaces
Marco Abbadini, Daniele Mundici
https://arxiv.org/abs/2508.21500 https://arxiv.org/pdf/2508.21500

Unital Specker $\ell$-groups and boolean multispaces
As a topological generalization of the notion of multiset, a boolean multispace is a boolean space $X$ with a continuous function $u\colon X\to \mathbb Z_{>0}$, where $\mathbb Z_{>0}=\{1,2,\dots\}$ has the discrete topology. In this paper the category of boolean multispaces and continuous multiplicity-decreasing morphisms with respect to the divisibility order is shown to be dually equivalent to the category of unital Specker $\ell$-groups and unital $\ell$-homomorphisms. This result extends St…

Applications of Borel-definable homological algebra to locally compact groups
Martino Lupini
https://arxiv.org/abs/2509.25474 https://arxiv.org/pdf/2509.25…

Applications of Borel-definable homological algebra to locally compact groups
We show that the $\mathrm{Hom}$ functor from the category $\mathbf{LCPAb}$ of locally compact Polish abelian groups to the category $\mathbf{PAb}$ of Polish abelian groups has a total right derived functor, improving on Hoffmann and Spitzweck's construction of its cohomological right derived functor. We also apply the description of the left heart of subcategories of $\mathbf{PAb}$ in terms of groups with a Polish cover and Borel-definable group homomorphisms to completely characterize the in…

Affine representations of rational and pretzel knots
Javier Mart\'inez
https://arxiv.org/abs/2510.02077 https://arxiv.org/pdf/2510.02077

Affine representations of rational and pretzel knots
We construct and study representations of rational and pretzel tangle and knot groups into the affine group $\mathrm{AGL}(1,\mathbb{C})$, via a TQFT that is valued in the category of spans of singular vector bundles over $\mathbb{C}^{\ast}$. For these families, we derive closed-form expressions for their Alexander polynomials and establish bounds on their zeros. Finally, we specialize the functor at $t=-1$ and analyze colorings of rational tangles in terms of spans of complex vector spaces.

Theory overview: electroweak emission from heavy-ion collisions
Greg Jackson
https://arxiv.org/abs/2509.00262 https://arxiv.org/pdf/2509.00262

Theory overview: electroweak emission from heavy-ion collisions
An important class of observables in the heavy-ion collision programme concerns probes which are not sensitive to the prevailing strong interactions of QCD. The emission of photons, weak gauge bosons, and leptons fall into this category. Here I will describe the current status of such investigations, focusing on the emerging theoretical picture and its uncertainties.

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- The ribbon category of representations of a crossed module
Ony Aubril
http…

Topological Vector Spaces
Pierre Colmez, Wies{\l}awa Nizio{\l}
https://arxiv.org/abs/2509.25981 https://arxiv.org/pdf/2509.25981

Topological Vector Spaces
Motivated by applications to duality theorems for $p$-adic pro-étale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full subcategories, both the category of (topologically) bounded algebraic Vector Spaces and the category of perfect complexes on the Fargues-Fontaine curve. Vector Spaces coming from $p$-adic pro-étale cohomology of smooth partially proper rigid analytic varieties are…

Silting reduction, relative AGK's construction and Higgs construction
Yilin Wu
https://arxiv.org/abs/2510.00470 https://arxiv.org/pdf/2510.00470…

Silting reduction, relative AGK's construction and Higgs construction
We introduce the notion of a Calabi--Yau quadruple as a generalization of Iyama--Yang's Calabi--Yau triple. For each \((d+1)\)-Calabi--Yau quadruple, we show that the associated Higgs category is a \(d\)-Calabi--Yau Frobenius extriangulated category, which moreover admits a canonical \(d\)-cluster-tilting subcategory. Concrete examples arise from the construction of relative cluster categories and Higgs categories in the setting of ice quivers with potentials, as well as from the singularity ca…

Functional programming isn't just for Haskell developers. It's for #PHP developers, too. "Thinking Functionally in PHP" is available from LeanPub.
https://leanpub.com/thinking-functiona

Thinking Functionally in PHP
Functional programming in PHP 7.4, with a side of category theory and monads accessible to everyone.

$C^0$-rigidity of Legendrians and coisotropics via sheaf quantization
Tomohiro Asano, Yuichi Ike, Christopher Kuo, Wenyuan Li
https://arxiv.org/abs/2510.01746 https://

$C^0$-rigidity of Legendrians and coisotropics via sheaf quantization
We prove that in the standard cosphere bundle, for any contact homeomorphism in the closure of the compactly supported contactomorphism group, when the image of a coisotropic submanifold (not necessarily properly embedded) is smooth, it is still coisotropic. Moreover, when contactomorphisms in the sequence are in the identity component and the image of a Legendrian is smooth, the Maslov data is preserved, and the category of sheaves with singular support on the Legendrian and the microstalk cor…

Joins of closed sublocales are not always a coframe
Igor Arrieta
https://arxiv.org/abs/2510.00987 https://arxiv.org/pdf/2510.00987

Joins of closed sublocales are not always a coframe
Given a locale $L$, the collection $\mathsf{S}_c(L)$ of joins of closed sublocales forms a frame--somewhat unexpectedly, as it is naturally embedded in the coframe of all sublocales of $L$, where by coframe we mean the order-theoretic dual of a frame. This construction has attracted attention in point-free topology: as a maximal essential extension in the category of frames, for its (non-)functorial properties, its relation to canonical extensions and exact filters of frames, etc. A central o…

Bridging Human Cognition and AI: A Framework for Explainable Decision-Making Systems
N. Jean, G. Le Pera
https://arxiv.org/abs/2509.02388 https://arxiv.org…

Bridging Human Cognition and AI: A Framework for Explainable Decision-Making Systems
Explainability in AI and ML models is critical for fostering trust, ensuring accountability, and enabling informed decision making in high stakes domains. Yet this objective is often unmet in practice. This paper proposes a general purpose framework that bridges state of the art explainability techniques with Malle's five category model of behavior explanation: Knowledge Structures, Simulation/Projection, Covariation, Direct Recall, and Rationalization. The framework is designed to be applicabl…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory
Samuele Pollaci, Babis Kostopoulos, Marc Denecker, Bart Bogaerts

Classification of Thouless pumps with non-invertible symmetries and implications for Floquet phases
Yabo Li, Matteo Dell'acqua, Aditi Mitra
https://arxiv.org/abs/2510.01626 …

Classification of Thouless pumps with non-invertible symmetries and implications for Floquet phases
We study symmetry preserving adiabatic and Floquet dynamics of one-dimensional systems. Using quasiadiabatic evolution, we establish a correspondence between adiabatic cycles and invertible defects generated by spatially truncated Thouless pump operators. Employing the classification of gapped phases by module categories, we show that the Thouless pumps are classified by the group of autoequivalences of the module category. We then explicitly construct Thouless pump operators for minimal lattic…

🏆 Counting down to the European Digital Connectivity Awards 2025!
Next week, the winners will be announced—and we’re honoured that GÉANT’s GN4-3N project is a finalist in the “Cross-border and international connectivity” category.
This recognition reflects the collaborative effort of the EU, GÉANT and our community of European NRENs to build a more inclusive, terabit-ready, and fully sovereign network infrastructure for Europe’s

Category Theory for Supercomputing: The Tensor Product of Linear BSP Algorithms
Thomas Koopman, Rob H. Bisseling, Sven-Bodo Scholz
https://arxiv.org/abs/2510.00979 https://

Category Theory for Supercomputing: The Tensor Product of Linear BSP Algorithms
We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous Parallel (BSP) -- that decomposes parallel algorithms into so-called supersteps that are one of two types: a computation superstep that only does local computations, or a communication superstep that only communicates between processors. We connect each type …

Category-Level Object Shape and Pose Estimation in Less Than a Millisecond
Lorenzo Shaikewitz, Tim Nguyen, Luca Carlone
https://arxiv.org/abs/2509.18979 https://

Transparent Semantic Spaces: A Categorical Approach to Explainable Word Embeddings
Ares Fabregat-Hern\'andez (Valencian Research Institute for Artificial Intelligence, Universidad Internacional de Valencia), Javier Palanca (Valencian Research Institute for Artificial Intelligence), Vicent Botti (Valencian Research Institute for Artificial Intelligence, valgrAI)

Transparent Semantic Spaces: A Categorical Approach to Explainable Word Embeddings
The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $ Ł_{T} $ and $ ¶_{T} $, providing schematic representations of the semantics of a text $ T $, and reframing the selection of the element with maximum probability as a categorical notion. Additionally, the monoidal category $ ¶_{T} $ is constructed to visualize various meth…

Open 2D TFTs admit initial open-closed extensions
Shaul Barkan, Jan Steinebrunner, Adela YiYu Zhang
https://arxiv.org/abs/2509.02553 https://arxiv.org/pdf/…

Open 2D TFTs admit initial open-closed extensions
We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology object of its value at the disk. As a corollary, we obtain an action of the moduli spaces of surfaces on the Hochschild homology object of $E_1$-Calabi-Yau algebras. This provides a space level refinement of previous work of Costello over $\mathbb{Q}$ and Wahl…

Rapidly intensifying Hurricane Erin becomes historic storm due to strengthening https://arstechnica.com/science/2025/08/hurricane-erin-sets-early-season-intensification-record-becomes-category-5-storm/

Hurricane Erin sets early season intensification record, becomes Category 5 storm
The good news is that, for now, Erin appears unlikely to directly strike land.

Affine vertex operator superalgebra $L_{\hat{sl(2|1)}}(\mathcal{k},0)$ at boundary admissible level
Huaimin Li, Qing Wang
https://arxiv.org/abs/2510.00679 https://

Affine vertex operator superalgebra $L_{\hat{sl(2|1)}}(\mathcal{k},0)$ at boundary admissible level
Let $L_{\widehat{sl(2|1)}}(\mathcal{k},0)$ be the simple affine vertex operator superalgebra associated to the affine Lie superalgebra $\widehat{sl(2|1)}$ with admissible level $\mathcal{k}$. We conjecture that $L_{\widehat{sl(2|1)}}(\mathcal{k},0)$ is rational in the category $\mathcal{O}$ at boundary admissible level $\mathcal{k}$ and there are finitely many irreducible weak $L_{\widehat{sl(2|1)}}(\mathcal{k},0)$-modules in the category $\mathcal{O}$, where the irreducible…

Holistic Order Prediction in Natural Scenes
Pierre Musacchio, Hyunmin Lee, Jaesik Park
https://arxiv.org/abs/2510.01704 https://arxiv.org/pdf/2510.01704

Holistic Order Prediction in Natural Scenes
Even in controlled settings, understanding instance-wise geometries is a challenging task for a wide range of visual models. Although specialized systems exist, modern arts rely on expensive input formats (category labels, binary segmentation masks) and inference costs (a quadratic amount of forward passes). We mitigate these limitations by proposing InstaFormer, a network capable of holistic order prediction. That is, solely given an input RGB image, InstaFormer returns the full occlusion and …

McKinsey-Tarski algebras and Raney extensions
Guram Bezhanishvili, Ranjitha Raviprakash, Anna Laura Suarez, Joanne Walters-Wayland
https://arxiv.org/abs/2509.01233 https://

McKinsey-Tarski algebras and Raney extensions
We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing the construction of the Funayama envelope of a frame. The resulting notion of the $T_0$-hull of a Raney extension generalizes that of the $T_D$-hull of a frame.

A weather system that is forecast to become Tropical Storm Imelda later on Sunday before approaching the coast of South Carolina as a hurricane in the coming days was causing disruption in the Bahamas and nearby islands.
Meanwhile, Hurricane Humberto weakened very slightly but remained a strong category 4 storm in the Atlantic, threatening Bermuda.
South Carolina’s governor, Henry McMaster, urged people to monitor the weather closely and stay alert.
And in North Carolina, …

On the representation type of a finite tensor category
Petter Andreas Bergh, Karin Erdmann, Julia Yael Plavnik, Sarah Witherspoon
https://arxiv.org/abs/2509.20853 https://

On the representation type of a finite tensor category
Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the category is of wild representation type. In particular, if the Krull dimension of the cohomology ring of the finite tensor category is at least three, then this category is wild.

The Balmer spectrum of Voevodsky motives and pure symbols
Alexander Vishik
https://arxiv.org/abs/2509.00584 https://arxiv.org/pdf/2509.00584

The Balmer spectrum of Voevodsky motives and pure symbols
In this article we introduce invariants of points of the Balmer spectrum of the Voevodsky motivic category whose values are "light Rost cycle submodules" of the module of pure symbols in Milnor's K-theory (mod 2). As an application, we show that isotropic points of the Balmer spectrum are closed. We also introduce the notion of points of a boundary type and show that this class contains isotropic points, but not the etale one.

On integral extensions between the abelianization functor and its symmetric powers
Minkyu Kim, Christine Vespa
https://arxiv.org/abs/2509.02105 https://arx…

On integral extensions between the abelianization functor and its symmetric powers
This paper aims to study Ext-groups between certain functors defined on the category of finitely generated free groups. Rational Ext-groups between the abelianization functor and its symmetric powers are known, and are almost always equal to zero. Recently, using homotopical methods, Arone constructed an explicit bounded complex whose homology corresponds to the integral Ext-groups between the abelianization functor and its symmetric powers. The homology of this complex is far from being trivia…

Day 7: Brenda Romero
I hinted yesterday I'd be moving beyond a narrow definition of "author," so of course that means I'm going to include game designers. I'll definitely get back to some more traditional authors before I hit 20, but I wanted to mix things up early.
Brenda Romero is something of a celebrity in the niche culture that is the Game Developers Coherence, I like to imagine. Of course the misogyny there likely means many just pay attention to who her husband is, but she's a terrific designer in her own right, if not prolific.
Content warning: the Holocaust
To me her most outstanding game has always been "Train," which is an exhibition tabletop game in which players collaborate to load and unload cargo and move train cars around a board, with the stated objective of efficiently delivering cargo to meet certain collective goals. However, through both physical cues and in-game reveals, it becomes clear to players that the game they are playing stimulates the Holocaust, and the cargo they're moving is people being brought to extermination camps. The actual goal of the game is for the players to stop playing and walk away, or perhaps to play against the stated objective and gridlock the trains. Romero supervised play at the expos where it was presented, and intervened to stop the game if the players continued too far (in some cases not picking up on the hints offered because they had very little knowledge of the Holocaust as a historical event). I've never played the game myself; just heard Romero give a report about it, but the sheer genius of designing a game meant not to be played to help educate about a system within which defying the rules was the only ethical action earned her instant respect from me. Romero has a whole series of games in this vein about didn't historical events (not necessarily all designed to not be played), although last I checked in most are just at prototyping stages.
I've got other non-man game designers that will appear on this list, but Romero stood out to go first because she's a good example that you don't need to be someone prolific or widely-known to do great work; I'd bet most people have an author or two they respect who is not widely known (and I'll include at least one more from that category on this list).
#20AuthorsNoMen

Foundation Visual Encoders Are Secretly Few-Shot Anomaly Detectors
Guangyao Zhai, Yue Zhou, Xinyan Deng, Lars Heckler, Nassir Navab, Benjamin Busam
https://arxiv.org/abs/2510.01934

Foundation Visual Encoders Are Secretly Few-Shot Anomaly Detectors
Few-shot anomaly detection streamlines and simplifies industrial safety inspection. However, limited samples make accurate differentiation between normal and abnormal features challenging, and even more so under category-agnostic conditions. Large-scale pre-training of foundation visual encoders has advanced many fields, as the enormous quantity of data helps to learn the general distribution of normal images. We observe that the anomaly amount in an image directly correlates with the differenc…

Weight modules and gluing of sheaves on the flag variety
Pablo Boixeda Alvarez, Calder Morton-Ferguson
https://arxiv.org/abs/2509.25156 https://arxiv.org/p…

Weight modules and gluing of sheaves on the flag variety
We study a natural enlargement of the BGG Category O for a semisimple Lie algebra: the category of weight modules with trivial central character and finite-dimensional weight spaces supported on the root lattice. We give a geometric realization of this category as unipotently monodromic sheaves on the flag variety satisfying a singular support condition. We then explain that a derived version $\mathcal{D}$ of this category is Koszul dual to the Kazhdan-Laumon Category O, a different enlargement…

The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set
Arghan Dutta, Stefano Luneia, Martina Rovelli, Sam Silver
https://arxiv.org/abs/2509.21472 https:…

The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set
We provide an explicit and elementary construction of the Morita $(\infty,2)$-category of a monoidal category which satisfies minimal conditions. We construct it as a $3$-coskeletal $2$-complicial set, in which the vertices encode the monoids, the edges encode the bimodules, the triangles encode the bimodule maps out of a balanced tensor product, and tetrahedra encode composition of bimodule maps. The marked edges encode invertible bimodules, and the marked triangles encode bimodule isomorphism…

The category of propositional deductive systems
Ciro Russo
https://arxiv.org/abs/2508.19426 https://arxiv.org/pdf/2508.19426…

The category of propositional deductive systems
We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\mathcal{DS}_0$, of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\mathcal{DS}_0$ is precisely the de…

Replaced article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- On the category of Hopf braces
Ana Agore, Alexandru Chirvasitu
https://

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Vandenberg SFB Rocket Launch Schedule: Today & Upcoming - Space Launch Schedule
Vandenberg SFB Rocket Launch Schedule: Live Video Feed, Trajectory, Location, Booster Landing Information Today & Upcoming - Space Launch Schedule

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Silting reduction, relative AGK's construction and Higgs construction
Yilin Wu

arxiv_collab: Scientific collaborations in physics (1995-2005)
Collaboration graphs for scientists, extracted from the Los Alamos e-Print arXiv (physics), for 1995-1999 for three categories, and additionally for 1995-2003 and 1995-2005 for one category. For copyright reasons, the MEDLINE (biomedical research) and NCSTRL (computer science) collaboration graphs from this paper are not publicly available.
This network has 31163 nodes and 120029 edges.
Tags: Social, Collaborati…

Category Discovery: An Open-World Perspective
Zhenqi He, Yuanpei Liu, Kai Han
https://arxiv.org/abs/2509.22542 https://arxiv.org/pdf/2509.22542

Category Discovery: An Open-World Perspective
Category discovery (CD) is an emerging open-world learning task, which aims at automatically categorizing unlabelled data containing instances from unseen classes, given some labelled data from seen classes. This task has attracted significant attention over the years and leads to a rich body of literature trying to address the problem from different perspectives. In this survey, we provide a comprehensive review of the literature, and offer detailed analysis and in-depth discussion on differen…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Contraderived categories of CDG-modules
Leonid Positselski, Jan Stovicek
http…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Stratifying systems and Jordan-H\"{o}lder extriangulated categories
Thomas Br\"ustle, Souheila Hassoun, Amit Shah, Aran Tattar

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Permutation twisted cohomology, remixed
Sam K. Miller
https://

Combinatorics of monoidal actions in Lie-algebraic context
Volodymyr Mazorchuk, Xiaoyu Zhu
https://arxiv.org/abs/2509.01404 https://arxiv.org/pdf/2509.0140…

Combinatorics of monoidal actions in Lie-algebraic context
This paper is, essentially, a survey related to the problem of understanding the combinatorics of the action of the monoidal category of finite dimensional modules over a simple finite dimensional Lie algebra on various categories of Lie algebra modules. A special attention is payed to the Lie algebras $\mathfrak{sl}_2$ and $\mathfrak{sl}_3$. A few new general results are collected at the end.

Hurricane Erin strengthened into a fearsome Category 5 hurricane with sustained winds of 160 mph for much of the day on Aug. 16
as it traveled west just north of the Virgin Islands, according to the National Hurricane Center.
The hurricane is not expected to make a direct hit on the United States,
but will still drive dangerous surf conditions along the East Coast, said Michael Brennan, hurricane center director.
"The weather can be otherwise pretty nice to be at …

Hurricane Erin a Category 4 after briefly strengthening to fierce Category 5 storm
Hurricane Erin briefly strengthened into a Category 5 storm. It is not expected to make a direct hit on the U.S. but will create dangerous surf.

Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces
Enrique Mac\'ias-Virg\'os, Daniel Tanr\'e
https://arxiv.org/abs/2509.20210 https…

Subspace {L}usternik-{S}chnirelmann category of quasi-projective quaternionic spaces
Let $Q_n$ be the quasi-projective subspace of the symplectic group $\mathrm{Sp}(n)$. In this short note, we prove that the subspace Lusternik-Schnirelmann category of $Q_n$ in $\mathrm{Sp}(n)$ is 2. For that, we use a quaternionic logarithm, as Singhof did in the complex case for the determination of the Lusternik-Schnirelmann category of the unitary group. Our result generalizes the known case $n=2$ (by L. Fernández-Suárez, A. Gómez-Tato and D. Tanré) and has to be compared to the equali…

Permutation twisted cohomology, remixed
Sam K. Miller
https://arxiv.org/abs/2509.00954 https://arxiv.org/pdf/2509.00954

Permutation twisted cohomology, remixed
We generalize Balmer and Gallauer's (permutation) twisted cohomology ring, working towards an alternative deduction of the Balmer spectrum of the derived category of permutation modules for any finite $p$-group. The construction comes equipped with a canonical comparison map from the Balmer spectrum to the homogeneous spectrum of the twisted cohomology ring, which we deduce is injective and an open immersion when the twisted cohomology ring is noetherian. For elementary abelian $p$-groups, the …

[2025-10-02 Thu (UTC), 5 new articles found for math.CT Category Theory]
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[2025-10-03 Fri (UTC), 2 new articles found for math.CT Category Theory]
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Crosslisted article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- The ribbon category of representations of a crossed module
Ony Aubril
http…

Manifolds and Disc-presheaves
Alexander Kupers
https://arxiv.org/abs/2509.26392 https://arxiv.org/pdf/2509.26392 …

Manifolds and Disc-presheaves
This essay explains an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as well as recent applications demonstrating its strength.

[2025-09-03 Wed (UTC), 3 new articles found for math.CT Category Theory]
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[2025-09-02 Tue (UTC), no new articles found for math.CT Category Theory]
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Categorical realization of collapsing subsurfaces and perverse schobers
Li Fan, Suiqi Lu
https://arxiv.org/abs/2510.00104 https://arxiv.org/pdf/2510.00104

Categorical realization of collapsing subsurfaces and perverse schobers
We study the categorification of collapsed Riemann surfaces with quadratic differentials allowing arbitrary order zeros and poles via the Verdier quotient. We establish an isomorphism between the exchange graph of hearts in the quotient category and the exchange graph of mixed-angulations on the collapsed surface. This extends the work of Barbieri-Möller-Qiu-So, who studied Verdier quotients of 3-Calabi-Yau categories and collapsed surfaces without simple poles. We use two methods: a combinato…

Colored Petri Nets are Lax Double Functors
Jade Master, Joe Moeller
https://arxiv.org/abs/2510.01946 https://arxiv.org/pdf/2510.01946

Colored Petri Nets are Lax Double Functors
We give a characterization of colored Petri nets as lax double functors. Framing colored Petri nets in terms of category theory allows for canonical definitions of various well-known constructions on colored Petri nets. In particular, we show how morphisms of colored Petri nets may be understood as natural transformations. A result from folklore, which we sketch in the appendix, shows that lax double functors are equivalent to functors with codomain their former domain. We use this result to ch…

On the Orthogonal Projections
Jiarui Fei
https://arxiv.org/abs/2510.01615 https://arxiv.org/pdf/2510.01615

On the Orthogonal Projections
For any ${\rm E}$-rigid presentation $e$, we construct an orthogonal projection functor to ${\rm rep}(e^\perp)$ left adjoint to the natural embedding. We establish a bijection between presentations in ${\rm rep}(e^\perp)$ and presentations compatible with $e$. For quivers with potentials, we show that ${\rm rep}(e^\perp)$ forms a module category of another quiver with potential. We derive mutation formulas for the $δ$-vectors of positive and negative complements and the dimension vectors of si…

Crosslisted article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- The Morita $(\infty,2)$-category of a monoidal category as a $2$-complicial set
Arghan Dutta, Stefano Luneia, Martina Rovelli, Sam Silver

Anchored Planar Algebras and 3-Categorical Graphical Calculus
Brett Hungar
https://arxiv.org/abs/2509.00995 https://arxiv.org/pdf/2509.00995

Anchored Planar Algebras and 3-Categorical Graphical Calculus
Anchored planar algebras, a generalized notion of Vaughan Jones' planar algebras, have recently seen use in higher category theory, functional analysis, and TQFT applications. These algebras are equipped with a natural 3-dimensional graphical calculus. We compare this graphical calculus with the 3-dimensional graphical calculus associated to tricategories, and we show that anchored planar algebras can be thought of as living in a particular tricategory. This allows for more general techniques t…

Rational quiver representations: tame and wild
Fabian Januszewski
https://arxiv.org/abs/2510.00924 https://arxiv.org/pdf/2510.00924

Rational quiver representations: tame and wild
We study representation finite $K$-rational quivers over fields of characteristic $0$ and their indecomposable representations, exploiting that all Brauer obstructions for descent of representations are trivial in this case. Contrasting the tame case, we give an example of a simple quiver of wild representation type, where we realize every possible Brauer obstruction of a given Galois extension $L/K$ in the category of quiver representations over $L$.

Stable first order theories as simplicial profinite sets
Misha Gavrilovich
https://arxiv.org/abs/2510.00854 https://arxiv.org/pdf/2510.00854

Stable first order theories as simplicial profinite sets
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the standard definitions based on syntax, making them formally unnecessary. We view a complete first-order theory as a symmetric simplicial object in the category of profinite sets and open continuous maps, defined by the functor sending a finite set of variables int…

$ L_\infty $-spectral sequences for Hochschild cohomology
Jasper van de Kreeke
https://arxiv.org/abs/2508.21716 https://arxiv.org/pdf/2508.21716

$ L_\infty $-spectral sequences for Hochschild cohomology
Spectral sequences are a common tool to compute cohomology spaces, but higher structure is often lost on the way. In this article we exhibit a strategy to retain the higher structure on the cohomology, which works in case the chain complex with higher structure is presented as the twisting of a simpler chain complex by a Maurer-Cartan element. This works particularly well in case of the Hochschild complex of a minimal $ A_\infty $-category, where the Hochschild complex can be seen as the twisti…

Modules over the category of Jacobi diagrams in handlebodies
Mai Katada
https://arxiv.org/abs/2509.16230 https://arxiv.org/pdf/2509.16230

Modules over the category of Jacobi diagrams in handlebodies
The linear category $\mathbf{A}$ of Jacobi diagrams in handlebodies was introduced by Habiro and Massuyeau. We study the category of modules over the category $\mathbf{A}$. We generalize the adjunction given by Powell to an adjunction between the category of $\mathbf{A}$-modules and the category of modules over the linear PROP for Casimir Lie algebras by using the category $\mathbf{A}^{L}$ of extended Jacobi diagrams in handlebodies. Then we study subquotient $\mathbf{A}$-modules of $\mathbf{A}…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Arrow algebras
Benno van den Berg, Marcus Briet
https://

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Applications of Borel-definable homological algebra to locally compact groups
Martino Lupini

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Higher condensation theory
Liang Kong, Zhi-Hao Zhang, Jiaheng Zhao, Hao Zheng

Gorenstein-Projective Modules over the Ring of Dual Integers
Xiu-Hua Luo (Department of Mathematics Nantong University,Mathematical Sciences Florida Atlantic University), Markus Schmidmeier (Department of Mathematics Nantong University,Mathematical Sciences Florida Atlantic University)
https://arxiv.org/abs/2509.22091

Gorenstein-Projective Modules over the Ring of Dual Integers
The ring of dual integers is the bounded polynomial ring $\mathbb Z[ε]=\mathbb Z[T]/(T^2)$ with integer coefficients. We describe the (finitely generated) Gorenstein-projective $\mathbb Z[ε]$-modules as the torsionless $\mathbb Z[ε]$-modules, or equivalently, as the perfect differential structures of abelian groups. Moreover, the stable category of G-proj$\mathbb Z[ε]$ modulo projectives is shown to be equivalent to the orbit category $\mathcal D^b(\mathbb Z)/[1]$ of the derived category of…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Categorical quantum symmetries and ribbon tensor 2-categories
Hank Chen
https…

Symmetric monoidal extensions and graph cobordisms between finite sets
Andrea Bianchi
https://arxiv.org/abs/2509.22575 https://arxiv.org/pdf/2509.22575

Symmetric monoidal extensions and graph cobordisms between finite sets
Given a symmetric monoidal $(\infty,n)$-category $\mathcal{C}$ and a space $X$, we address the problem of explicitly describing the symmetric monoidal $(\infty,n)$-category freely obtained from $\mathcal{C}$ by adjoining $X$ new $n$-morphisms with prescribed sources and targets. We develop an apparatus of tools that allow one to detect in concrete situations such a free symmetric monoidal extension. As motivating application, we introduce a symmetric monoidal $(\infty,2)$-category ${\mathbb{G}\…

Special modules over Jordan algebras
Iryna Kashuba, Vera Serganova
https://arxiv.org/abs/2509.23070 https://arxiv.org/pdf/2509.23070

Special modules over Jordan algebras
In this paper we study special representations of finite-dimensional Jordan algebra $J$ whose $Rad^2 J=0$. For each Jordan algebra $J$ of this class we consider its Tits-Kantor-Koecher construction $TKK(J)$ and then associate to the latter a quiver with relations $Q$ such that the category of representations of $Q$ is isomorphic to the category of special representations of $J$.

Learners are Almost Free Compact Closed
Mitchell Riley
https://arxiv.org/abs/2509.20930 https://arxiv.org/pdf/2509.20930

Learners are Almost Free Compact Closed
The category of learners has a pleasant symmetric formulation when the morphisms are considered up to a coarser equivalence than the one originally described in the paper "Backprop as Functor". A quotient of this modified category gives a new construction of the free compact closed category on a symmetric monoidal category.

[2025-10-01 Wed (UTC), 2 new articles found for math.CT Category Theory]
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[2025-09-01 Mon (UTC), 2 new articles found for math.CT Category Theory]
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How to build a Hopf algebra
Theo Johnson-Freyd, David Reutter
https://arxiv.org/abs/2508.16787 https://arxiv.org/pdf/2508.16787

How to build a Hopf algebra
We construct a functor that inputs a retract in an $(\infty,3)$-category satisfying some adjunctibility conditions and outputs a Hopf algebra in a braided monoidal $(\infty,1)$-category. Provided the braided monoidal category is presentable, any Hopf algebra can be obtained in this way. Our functor specializes to - and provides a higher-categorical explanation for - the Tannakian reconstruction of a Hopf algebra from a monoidal category with duals and a fiber functor. Towards this end, we rev…

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Double categorical equivalences
Lyne Moser, Maru Sarazola, Paula Verdugo
h…

Galois Connections and Preradicals in Abelian Categories
Rogelio Fern\'andez-Alonso, Janeth Maga\~na, Martha Lizbeth Shaid Sandoval-Miranda, Valente Santiago-Vargas
https://arxiv.org/abs/2509.21564

Galois Connections and Preradicals in Abelian Categories
In this paper we define operations of preradicals of any abelian category. We define idempotent preradicals and radicals. We prove that every adjoint pair between abelian categories induces a Galois connection between the corresponding ordered collections of preradicals. If the abelian categories are bicomplete, we construct alpha and omega preradicals and study their respective preservation under the Galois connection. If a bicomplete abelian category is in addition locally small, then the cor…

The nine model category structures on the category of sets
Omar Antol\'in-Camarena, Tobias Barthel
https://arxiv.org/abs/2508.15731 https://arxiv.org/p…

The nine model category structures on the category of sets
We give a proof of the folklore theorem, attributed to Goodwillie, that there are precisely nine model structures on the category $\mathsf{Set}$ of sets. This result is deduced from a complete study of lifting problems and the ensuing classification of all weak factorization systems on $\mathsf{Set}$. Moreover, we determine the Quillen equivalences between these model structures and exhibit an explicit example of equivalent model structures that cannot be realized by a single Quillen adjunction.

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- The category of propositional deductive systems
Ciro Russo
https://…

Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets
J. Miguel Calder\'on, Alberto Gerardo Raggi-C\'ardenas, Itzel Rosas, Ram\'on H. Ruiz-Medina
https://arxiv.org/abs/2508.10162

Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets
A $\mathcal{C}$-set is a functor from the category $\mathcal{C}$ to the category of finite sets and functions. The category of $\mathcal{C}$-sets, $\mathcal{C} - \operatorname*{set}$, is defined as the category whose objects are $\mathcal{C}$-sets, and whose morphisms are natural transformations between them. In this document we provide some concise characterizations of groupoids in terms of their category of $\mathcal{C}$-sets.

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Coassociative structures on self-injective algebras
Alexandru Chirvasitu
h…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Homological invariant properties under cleft extensions
Li Liang, Yajun Ma, Gang Yang

[2025-09-30 Tue (UTC), 1 new article found for math.CT Category Theory]
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Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Formal category theory in $\infty$-equipments I
Jaco Ruit
https://

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Basic Category Theory
Tom Leinster
https://arxiv.org/ab…