Tootfinder

Coherence for Pseudo Commutative Monads
Diego Manco
https://arxiv.org/abs/2509.15101 https://arxiv.org/pdf/2509.15101…

Coherence for Pseudo Commutative Monads
We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a multifunctor. Furthermore, we prove that this multifunctor is pseudo symmetric. Our proof implies coherence results for both symmetric and non-symmetric pseudo commutative 2-monads conjectured by Hyland and Power.

Is there some category in which CassetteBoy can be nominated for an Oscar? This is brilliant:
https://youtu.be/C8uOPrU4B9s

$c$-structures and trace methods beyond connective rings
Ishan Levy, Vladimir Sosnilo
https://arxiv.org/abs/2509.14774 https://arxiv.org/pdf/2509.14774

$c$-structures and trace methods beyond connective rings
We introduce the notion of a $c$-category, which is a kind of category whose behaviour is controlled by connective ring spectra. More precisely, any $c$-category admits a finite step resolution by categories of compact modules over connective ring spectra. We introduce nilpotent extensions of $c$-categories, and show that they induce isomorphisms on truncating invariants, such as the fiber of the cyclotomic trace map. We show that for many stacks, the category of perfect complexes is naturally …

Added a zoom level to the Category page on the Exocortex-Log app. Can make the graphs look a lot cleaner now.
Looking back over the last 100 months here, we can see in general my social life is quite seasonal -- Festivals are a lot of social all weekend long and a couple of them in a month really bumps up the hours from my usual habit of sitting alone in a dark room pressing buttons.
The peak in 2019 is a summer filled with Glasto and Noisily and another festival or camping trip I don’t seem to have recorded the name of.
Then clearly visible is the drop-off in social activity as the COVID pandemic hit. Virtual-Social (IE zoom meetings and the like) picked up quite a bit around there but had died back to almost nothing way before the hours spent with actual people started to tick up.
Annoyingly, I have my biggest gap in data right on top of the pandemic there, where I failed to back up for months and then data became corrupted.
When the data-hole is over we see social life still not really returning until the middle of 2021 and not really getting back into stride until summer 2022.
It remains much lower now on average with lower peaks than before the pandemic too. Multiple reasons.
Work is pretty constant all the way though other than the data-hole. Dipping when I take time off for social mostly.
That data-hole is annoying. Back up your data kids.
#lifeLog #app #exocortexLog

"Craft a single network packet to obtain root": I had hoped that this type of vulnerability hat been eliminated.
At least, the Router Advertisement packets should generally not be able to cross routers.
Patch your #FreeBSD systems now.
#rtsol

Integrals for Bialgebras
Alessandro Ardizzoni, Claudia Menini, Paolo Saracco
https://arxiv.org/abs/2509.14823 https://arxiv.org/pdf/2509.14823

Integrals for Bialgebras
A well-known result by Larson and Sweedler shows that integrals on a Hopf algebra can be obtained by applying the Structure Theorem for Hopf modules to the rational part of its linear dual. This fact can be rephrased by saying that taking the space of integrals comes from a right adjoint functor from a category of modules to the category of vector spaces. This observation inspired the categorical approach that we advocate in this work, which yields to a new notion of integrals for bialgebras in…

Oriented Category Theory
David Gepner, Hadrian Heine
https://arxiv.org/abs/2510.10504 https://arxiv.org/pdf/2510.10504

Oriented Category Theory
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical dimension increases, classical category-theoretic concepts generally prove too rigid or fully break down and must be replaced by oriented versions, which allow more flexible notions of naturality and coherence. Oriented category theory provides a framework to addre…

'A New Category of Evidence.' Feds Cite ChatGPT Logs of Palisades Fire Suspect
https://www.pcmag.com/news/a-new-category-of-evidence-feds-cite-chatgpt-logs-of-palisades-fire-suspect

World Cup ticket prices.
#worldcup

Yesterday at the @… conference, the Brücke-Museum Berlin presented its digitization project on Karl Schmidt-Rottluff’s collection of objects from colonial contexts. All objects have been published on #wikiCommons, allowing everyone to contribute and r…

The Groupoid-syntax of Type Theory is a Set
Thorsten Altenkirch, Ambrus Kaposi, Szumi Xie
https://arxiv.org/abs/2509.14988 https://arxiv.org/pdf/2509.14988…

The Groupoid-syntax of Type Theory is a Set
Categories with families (CwFs) have been used to define the semantics of type theory in type theory. In the setting of Homotopy Type Theory (HoTT), one of the limitations of the traditional notion of CwFs is the requirement to set-truncate types, which excludes models based on univalent categories, such as the standard set model. To address this limitation, we introduce the concept of a Groupoid Category with Families (GCwF). This framework truncates types at the groupoid level and incorporate…

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 8361 nodes and 15751 edges.
Tags: Social, Collaboration…

CARGO: A Framework for Confidence-Aware Routing of Large Language Models
Amine Barrak, Yosr Fourati, Michael Olchawa, Emna Ksontini, Khalil Zoghlami
https://arxiv.org/abs/2509.14899

CARGO: A Framework for Confidence-Aware Routing of Large Language Models
As large language models (LLMs) proliferate in scale, specialization, and latency profiles, the challenge of routing user prompts to the most appropriate model has become increasingly critical for balancing performance and cost. We introduce CARGO (Category-Aware Routing with Gap-based Optimization), a lightweight, confidence-aware framework for dynamic LLM selection. CARGO employs a single embedding-based regressor trained on LLM-judged pairwise comparisons to predict model performance, with a…

Beyond 'Templates': Category-Agnostic Object Pose, Size, and Shape Estimation from a Single View
Jinyu Zhang, Haitao Lin, Jiashu Hou, Xiangyang Xue, Yanwei Fu
https://arxiv.org/abs/2510.11687

Beyond 'Templates': Category-Agnostic Object Pose, Size, and Shape Estimation from a Single View
Estimating an object's 6D pose, size, and shape from visual input is a fundamental problem in computer vision, with critical applications in robotic grasping and manipulation. Existing methods either rely on object-specific priors such as CAD models or templates, or suffer from limited generalization across categories due to pose-shape entanglement and multi-stage pipelines. In this work, we propose a unified, category-agnostic framework that simultaneously predicts 6D pose, size, and dense sha…

Daniel Carlson Moves Up in Raiders History https://www.si.com/nfl/raiders/daniel-carlson-las-vegas-justin-tucker-george-blanda

On the Coarse Lusternik-Schnirelmann Category of Groups
Aditya De Saha
https://arxiv.org/abs/2510.10367 https://arxiv.org/pdf/2510.10367

On the Coarse Lusternik-Schnirelmann Category of Groups
We introduce a coarse analog of the classical Lusternik-Schnirelmann category which we denote by $\text{c-cat}$, defined for metric spaces in the coarse homotopy category. This provides a new tool for studying large-scale topological properties of groups and spaces. We establish that $\text{c-cat}$ is a coarse homotopy invariant and prove a lower-bound $\text{p-cat}(Γ)\leq \text{c-cat}(Γ)$ for geometrically finite groups $Γ$, where $\text{p-cat}$ denotes the proper LS-category introduced in …

Cowboys’ Dak Prescott Top 3 in this cringeworthy QB category https://cowboyswire.usatoday.com/story/sports/nfl/cowboys/2025/10/11/cowboys-dak-prescott-top-three-cringeworthy-category/86609094007/

Give me your suggestions for "assassinated revolutionaries" missing from this #Wikipedia category.
#crowdsourcing

Monoidal categorification and quantum affine algebras III
Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park
https://arxiv.org/abs/2509.14552 https://a…

Monoidal categorification and quantum affine algebras III
Let $U_q'(\mathfrak{g})$ be an arbitrary quantum affine algebra of either untwisted or twisted type, and let $\mathscr{C}_{\mathfrak{g}}^0$ be its Hernandez-Leclerc category. We denote by $\mathsf{B}$ the braid group determined by the simply-laced finite type Lie algebra $ \mathsf{g}$ associated with $U_q'(\mathfrak{g})$. For any complete duality datum $\mathbb{D}$ and any sequence of simple roots of $\mathsf{g}$, we construct the corresponding affine cuspidal modules and affine determinantial …

[2025-09-19 Fri (UTC), 1 new article found for math.CT Category Theory]
toXiv_bot_toot

Natural transformations between braiding functors in the Fukaya category
Yujin Tong
https://arxiv.org/abs/2511.10462 https://arxiv.org/pdf/2511.10462 https://arxiv.org/html/2511.10462
arXiv:2511.10462v1 Announce Type: new
Abstract: We study the space of $A_\infty$-natural transformations between braiding functors acting on the Fukaya category associated to the Coulomb branch $\mathcal{M}(\bullet,1)$ of the $\mathfrak{sl}_2$ quiver gauge theory. We compute all cohomologically distinct $A_\infty$-natural transformations $\mathrm{Nat}(\mathrm{id}, \mathrm{id})$ and $\mathrm{Nat}(\mathrm{id}, \beta_i^-)$, where $\beta_i^-$ denotes the negative braiding functor. Our computation is carried out in a diagrammatic framework compatible with the established embedding of the KLRW category into this Fukaya category. We then compute the Hochschild cohomology of the Fukaya category using an explicit projective resolution of the diagonal bimodule obtained via the Chouhy-Solotar reduction system, and use this to classify all cohomologically distinct natural transformations. These results determine the higher $A_\infty$-data encoded in the braiding functors and their natural transformations, and provide the first step toward a categorical formulation of braid cobordism actions on Fukaya categories.
toXiv_bot_toot

今のうちから警官が呼び止めて指導している地域はあるようだ。早いところ気を引き締めておいた方がよさそう。
https://news.ntv.co.jp/n/mmt/category/society/mm30cecd28feeb4721bda2ee91ea484b31

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…

The Golden Globes' inaugural best podcast award nominations avoided controversy by passing on popular politics-related podcasts and personalities like Joe Rogan (Mark Kennedy/Associated Press)
https://apnews.com/article/golden-globes-podcast-cat…

Golden Globes' inaugural best podcast award nominees avoid politics
The Golden Globes have introduced a best podcast category that's likely to spark conversations. On Monday, the Globes announced six nominees, including “Armchair Expert” and “SmartLess.” They represented a mix of news, advice and celebrity interviews. Notably absent are politically oriented podcasts like “The Joe Rogan Experience” and “Pod Save America.” Experts suggest the Globes aim to avoid controversy by focusing on entertainment. The selection process has raised questions, …

The Year in Review I didn't know existed is in!
The #NYTGames Review 2025

Then, out of a sudden, my photo from Abotak abortion clinic in Warsaw was highlighted in Editorial / General News category of Budapest International Foto Awards.
Yay!
https://budapestfotoawards.com/winners/bifa/2025/9038/

Lax functoriality of Hochschild cochain complex
Yang Han, Xukun Wang
https://arxiv.org/abs/2509.14620 https://arxiv.org/pdf/2509.14620

Lax functoriality of Hochschild cochain complex
Unlike the Hochschild chain complex of an algebra, the Hochschild cochain complex of an algebra is not functorial. Nonetheless, we show that the Hochschild cochain complex of an algebra even a dg category is of lax functoriality, i.e., there exists a lax functor from bicategory of dg categories to bicategory of $B_\infty$-algebras which sends every dg category to its Hochschild cochain complex. This result is a homotopy version of the lax functoriality of center of an algebra obtained by Davydo…

"Before we go into what is missing, let us take a moment to understand why this partial story is so popular. Many software engineers do not engage with the broad “software engineering literature” very much: through the act of reading this magazine you are placing yourself at the pinnacle of software engineering curiosity!"
https…

The Other Side Of The Card
If you ask many developers what a "user story" is, you will be told that it is a software requirement expressed using a prescribed formula: "As a category of person, I want to do a thing so that some goal is attained."

On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
Rustam Steingart
https://arxiv.org/abs/2510.12533 https://arxiv.org/pd…

On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension
Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and de Rham objects in explicit terms. When $E$ is a proper extension, we give a new description of the category in terms of compatible tuples of $\mathbf{B}_e$-modules, which allows us to compute Galois cohomology in terms of an explicit Čech complex which can…

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

"The Securing American Funding and Expertise from Adversarial Research Exploitation (SAFE) Act would deny federal funding to any U.S. scientist who collaborates with anyone “affiliated with a hostile foreign entity,” a category that includes four countries: China, Russia, Iran, and North Korea. The prohibited activities would include joint research, co-authorship on papers, and advising a foreign graduate student or postdoctoral fellow. The language is retroactive, meaning any interactions during the previous 5 years could make a scientist ineligible for future federal funding."
https://www.science.org/content/article/u-s-congress-considers-sweeping-ban-chinese-collaborations

From Abelianization to Tangent Categories
Sacha Ikonicoff, Jean-Simon Pacaud Lemay, Tim Van der Linden
https://arxiv.org/abs/2510.12324 https://arxiv.org/p…

From Abelianization to Tangent Categories
A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of the classical tangent bundle of smooth manifolds. In this paper, we show that, surprisingly, the category of groups is a tangent category whose tangent bundle functor is induced by abelianization and whose differential bundles correspond to abelian groups. We generalize this construction by introducing the concept of…

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

Today in starling-el, the ability to set spending categories! Our first non-read operation. It's much nicer doing this in #emacs IMO!

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 8361 nodes and 15751 edges.
Tags: Social, Collaboration…

Centralizers of discrete Temperley-Lieb-Jones subfactors
Corey Jones, Emily McGovern
https://arxiv.org/abs/2510.12675 https://arxiv.org/pdf/2510.12675

Centralizers of discrete Temperley-Lieb-Jones subfactors
Discrete, unimodular inclusions of factors $(N\subseteq M, E)$ with $N$ of type $\rm{II}_{1}$ have a natural notion of standard invariant, generalizing the finite index case. When the unitary tensor category of $N$-$N$ bimodules generated by $_{N}L^{2}(M, τ\circ E)_{N}$ is equivalent to the Temperley-Lieb-Jones category $\text{TLJ}(δ)$, the associated discrete standard invariants are classified in terms of fair and balanced $δ$-graphs. Many examples of these subfactors naturally arise in the…

Added a category manager and category state section to the Exocortex Log app.
Have now organized and cleaned up the categories in my ten year database and so we can get some views of the time spent in each category.
We see that through September and October I was in a routine of work and slack with a bit of social a couple of times a week, until the end of November when I went away for social at a conference all weekend. I saw a demo there of a person using Shakespeare, and then when I got back started doing some vibe-coding, shown in in Red.
A break from that to go away at the weekend to a long social party then finish it off and publish a few days ago, since when Vibe Coding has dropped off a little.
#lifeLog #app #exocortexLog

Totally scientific survey about how many Canadians have experienced the #NorthernLights. Non-Canadians are encouraged to participate because we are an inclusive nation. Please boost for national/international coverage.
How many times have you watched the Northern Lights? (Note: I'm in the Two to Nine category)
Never
Once
Two to Nine Times
More Than 10 Times
So many I don't even look up anymore.

A profile of Mercor CEO Brendan Foody, who says Mercor is creating a new category of work; Mercor hit $500M ARR in September and pays contractors $1.5M daily (Rya Jetha/The San Francisco Standard)
https://sfstandard.com/2025/11/07/san-franci…

San Francisco’s youngest billionaires are betting on a new kind of job boom
Mercor’s 22-year-old CEO Brendan Foody imagines a future in which white-collar contractors earn riches teaching machines to behave like humans.

The fundamental junk theorem of material set theory: every discrete category is concrete.

Registration for HRM26 Hellenic Mountain Race 2026 is now live. May 23-30, 2026
https://themountainraces.eventrac.co.uk/e/hellenic-mountain-race-14449

Hellenic Mountain Race
Welcome to the application process for Hellenic Mountain Race 2026 The application process is divided into the following two stages STAGE ONE: Choose your entry category and submit your personal information to receive a confirmation email with a...

Day 20: bell hooks.
Despite having decided to continue to 30, number 20 feels important, and hooks gets the spot in part because I haven't yet included a non-fiction feminist author, which feels like an obvious thing to include on such a list. The one category of author being bumped out of the first 20 here is anime writers, but I'll follow up with one of them, along with more academics and mangaka who I've been itching to include.
In any case, hooks is absolutely legendary as a feminist writer for good reason, and as a teacher I've especially appreciated her writing on pedagogy like "Teaching to Transgress: Education as the Practice of Freedom" and "Teaching Critical Thinking: Practical Wisdom". These have challenged me to teach at a higher level, and while I'm not sure I've completely succeeded, they're important to me. They also pair well with Paolo Friere's "Pedagogy of the Oppressed", but hooks always seems to be focused on very practical advice and it's incredibly direct in her writing, even though her advice isn't always straightforward to implement. In fact, that's one of the things I value about her writing: when the truth is complicated or the real work is messy interpersonal relationships that need to be negotiated with each student, she's not afraid to say so and give good advice for navigating those waters instead of trying to dispense simple-seeming platitudes or formulas for success that paper over the deeper issues. Her concern has always been truth, rather than simplicity or audience comfort and the popularity it might seem to entail, which I think is part of why her legacy endures so well.
#20AuthorsNoMen
#30AuthorsNoMen

“Most anticipated game” why’s that even a category, but like if it is it should at least be Witcher 4 wtf
#TGA #TheGameAwards

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/

The Hidden DNA of LLM-Generated JavaScript: Structural Patterns Enable High-Accuracy Authorship Attribution
Norbert Tihanyi, Bilel Cherif, Richard A. Dubniczky, Mohamed Amine Ferrag, Tam\'as Bisztray
https://arxiv.org/abs/2510.10493

The Hidden DNA of LLM-Generated JavaScript: Structural Patterns Enable High-Accuracy Authorship Attribution
In this paper, we present the first large-scale study exploring whether JavaScript code generated by Large Language Models (LLMs) can reveal which model produced it, enabling reliable authorship attribution and model fingerprinting. With the rapid rise of AI-generated code, attribution is playing a critical role in detecting vulnerabilities, flagging malicious content, and ensuring accountability. While AI-vs-human detection usually treats AI as a single category we show that individual LLMs le…

Cartesian closedness of the category of real-valued sets, I
Lili Shen, Jian Zhang
https://arxiv.org/abs/2510.12108 https://arxiv.org/pdf/2510.12108

Cartesian closedness of the category of real-valued sets, I
Let $[0,1]_*$ be the unit interval $[0,1]$ equipped with a continuous t-norm $*$. It is shown that the category of $[0,1]_*$-sets is cartesian closed if, and only if, $*$ is the minimum t-norm on $[0,1]$.

今のうちから警官が呼び止めて指導している地域はあるようだ。早いところ気を引き締めておいた方がよさそう。
https://news.ntv.co.jp/n/mmt/category/society/mm30cecd28feeb4721bda2ee91ea484b31

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…

Causal Inspired Multi Modal Recommendation
Jie Yang, Chenyang Gu, Zixuan Liu
https://arxiv.org/abs/2510.12325 https://arxiv.org/pdf/2510.12325

Causal Inspired Multi Modal Recommendation
Multimodal recommender systems enhance personalized recommendations in e-commerce and online advertising by integrating visual, textual, and user-item interaction data. However, existing methods often overlook two critical biases: (i) modal confounding, where latent factors (e.g., brand style or product category) simultaneously drive multiple modalities and influence user preference, leading to spurious feature-preference associations; (ii) interaction bias, where genuine user preferences are m…

To be fair — there is another country in the same category as the UK.
Yes, Canada — I’m looking at you. https://pubeurope.com/@europesays/115524476481545848

Europe Says (@europesays@pubeurope.com)
Attached: 1 image https://www.europesays.com/2559172/ God, I need a pint. Heresy, I say. #GreatBritish #GreatBritishMemes #Memes #UnitedKingdom

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://

$F$-divided bundles on normal $F$-finite schemes
Adrian Langer, Lei Zhang
https://arxiv.org/abs/2510.10582 https://arxiv.org/pdf/2510.10582

$F$-divided bundles on normal $F$-finite schemes
In this paper we study $F$-divided bundles on irreducible Noetherian normal $F$-finite $\mathbb{F}_p$-schemes and we show that their Tannakian category is governed by the behaviour at the generic point. In particular, if $U\subset X$ is an open subset of a normal variety defined over an algebraically closed field then the corresponding homomorphism of $F$-divided fundamental groups is faithfully flat. This is analogous to a known fact about the topological fundamental group of an open subset of…

Extensions between functors from Jacobi diagrams in handlebodies
Mai Katada
https://arxiv.org/abs/2510.09625 https://arxiv.org/pdf/2510.09625

Extensions between functors from Jacobi diagrams in handlebodies
The first Ext-groups between Schur functors in the category of modules over the $\Bbbk$-linearization $\Bbbk\mathbf{gr}^{\operatorname{op}}$ of the opposite of the category of finitely generated free groups are computed for a filed $\Bbbk$ of characteristic $0$. The $\Bbbk$-linear category $\mathbf{A}$ of Jacobi diagrams in handlebodies, which was introduced by Habiro and Massuyeau, has an $\mathbb{N}$-grading whose degree $0$ part identifies with the category $\Bbbk\mathbf{gr}^{\operatorname{o…

The homotopy type of the Poincar\'e cobordism category for surfaces
Az\'elie Picot
https://arxiv.org/abs/2510.07659 https://arxiv.org/pdf/2510.0765…

The homotopy type of the Poincaré cobordism category for surfaces
We define a version of the surface cobordism category $\mathrm{Cob}_2^{\mathrm{SG}}(X)$ over a base space $X$ where surfaces are considered up to self homotopy equivalences instead of diffeomorphisms. We prove the induced functor $B\mathrm{Cob}_2^{\mathrm{SG}}(-): \mathcal{S} \rightarrow \mathcal{S}$ is not $1$-excisive. We show its first derivative $\partial_1 B\mathrm{Cob}_2^{\mathrm{SG}}(-)$ in the Goodwillie sense is equivalent to a Thom spectrum over $B\mathrm{haut}_*^+(S^2)$.

Equivariant Eilenberg-Watts theorem for module coalgebras
Taiki Shibata (Okayama University of Science), Kenichi Shimizu (Shibaura Institute of Technology)
https://arxiv.org/abs/2510.07969

Equivariant Eilenberg-Watts theorem for module coalgebras
For coalgebras $C$ and $D$, Takeuchi proved that the category of linear functors from $\mathfrak{M}^C$ to $\mathfrak{M}^D$ preserving small coproducts is equivalent to the category of $C$-$D$-bicomodules, where $\mathfrak{M}^C$ for a coalgebra $C$ means the category of right $C$-comodules. We formulate and prove an equivariant version of this result for module coalgebras over a bialgebra. As an application, for a bialgebra $H$, we establish an equivalence of the 2-category of a particular class…

Monoidal model structures over infinite groups
Ioannis Emmanouil, Olympia Talelli
https://arxiv.org/abs/2510.08195 https://arxiv.org/pdf/2510.08195

Monoidal model structures over infinite groups
The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a plethora of infinite groups G, for which the category of kG-modules (where k is a commutative coherent ring of finite global dimension) admits a monoidal model structure, in the sense of Hovey, whose associated homotopy category is a compactly generated tensor …

Substitution Without Copy and Paste
Thorsten Altenkirch (University of Nottingham), Nathaniel Burke (Imperial College London), Philip Wadler (University of Edinburgh)
https://arxiv.org/abs/2510.12304

Substitution Without Copy and Paste
Defining substitution for a language with binders like the simply typed $λ$-calculus requires repetition, defining substitution and renaming separately. To verify the categorical properties of this calculus, we must repeat the same argument many times. We present a lightweight method that avoids repetition and that gives rise to a simply typed category with families (CwF) isomorphic to the initial simply typed CwF. Our paper is a literate Agda script.

DiT-VTON: Diffusion Transformer Framework for Unified Multi-Category Virtual Try-On and Virtual Try-All with Integrated Image Editing
Qi Li, Shuwen Qiu, Julien Han, Xingzi Xu, Mehmet Saygin Seyfioglu, Kee Kiat Koo, Karim Bouyarmane
https://arxiv.org/abs/2510.04797

DiT-VTON: Diffusion Transformer Framework for Unified Multi-Category Virtual Try-On and Virtual Try-All with Integrated Image Editing
The rapid growth of e-commerce has intensified the demand for Virtual Try-On (VTO) technologies, enabling customers to realistically visualize products overlaid on their own images. Despite recent advances, existing VTO models face challenges with fine-grained detail preservation, robustness to real-world imagery, efficient sampling, image editing capabilities, and generalization across diverse product categories. In this paper, we present DiT-VTON, a novel VTO framework that leverages a Diffus…

Without real vector spaces all regulators are rational
Oliver Braunling
https://arxiv.org/abs/2510.10816 https://arxiv.org/pdf/2510.10816

Without real vector spaces all regulators are rational
Every LCA group has a Haar measure unique up to rescaling by a positive scalar. Clausen has shown that the Haar measure describes the universal determinant functor of the category LCA in the sense of Deligne. We show that when only working with LCA groups without allowing real vector spaces, any conceivable determinant functor is unique up to rescaling by at worst rational values. As a result, no transcendental real nor p-adic regulators could ever show up in special L-value conjectures (as in …

Reconstruction of tensor categories of type $G_2$
Lilit Martirosyan, Hans Wenzl
https://arxiv.org/abs/2510.09922 https://arxiv.org/pdf/2510.09922

Reconstruction of tensor categories of type $G_2$
We prove that any non-symmetric ribbon tensor category $\mathcal{C}$ with the fusion rules of the compact group of type $G_2$ needs to be equivalent to the representation category of the corresponding Drinfeld-Jimbo quantum group for $q$ not a root of unity. We also prove an analogous result for the corresponding finite fusion tensor categories.

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Measuring Comodules and Enrichment
Martin Hyland, Ignacio Lopez Franco, Christina Vasilakopoulou

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, …

Generalized Clifford algebras, weighted polynomial laws, and adjunction
Nguyen Xuan Bach
https://arxiv.org/abs/2510.06560 https://arxiv.org/pdf/2510.06560

Generalized Clifford algebras, weighted polynomial laws, and adjunction
In this paper, we study Clifford algebra construction from the perspective of adjunctions motivated by the general framework of Krashen and Lieblich. We introduce a category of weighted polynomial laws whose associated Clifford algebra functor is a left adjoint on this category. We give a notion of lifting weighted polynomial laws that generalize Krashen and Lieblich's explicit constructions. As another application, we give the construction of derived Clifford algebras for derived homogeneous p…

Stability Conditions and Algebraic Hearts for Acyclic Quivers
Takumi Otani, Dongjian Wu
https://arxiv.org/abs/2510.08961 https://arxiv.org/pdf/2510.08961…

Stability Conditions and Algebraic Hearts for Acyclic Quivers
We study stability conditions on the derived category of a finite connected acyclic quiver. We prove that, for any stability condition on the derived category, its heart can be obtained from an algebraic heart by a rotation of phases. Consequently, we establish the connectedness of the space of stability conditions. Furthermore, we prove that every stability condition $σ$ admits a full $σ$-exceptional collection.

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…

Some Properties of Homology and Exactness of Nomura's Homology Sequences in a Grandis Homological Category
Yaroslav Kopylov, Vadim Leshkov
https://arxiv.org/abs/2510.11672 h…

Some Properties of Homology and Exactness of Nomura's Homology Sequences in a Grandis Homological Category
We consider Lambek's invariants $\text{Ker}$ and $\text{Im}$ for commutative squares in Grandis homological categories. We prove that Nomura's null sequences exist in such categories and find sufficienct conditions for their exactness. We also prove the coincidence of left and right homology in Grandis homological categories.

Generalised Joyal disks and $\Theta_d$-colored $(d 1)$-operads
Boris Shoikhet
https://arxiv.org/abs/2510.05813 https://arxiv.org/pdf/2510.05813

Generalised Joyal disks and $Θ_d$-colored $(d+1)$-operads
In this paper, we propose a method for constructing a colored $(d+1)$-operad $\mathbf{seq}_d$ in $\mathrm{Sets}$, in the sense of Batanin [Ba1,2], whose category of colors (=the category of unary operations) is the category $Θ_d$, dual to the Joyal category of $d$-disks [J], [Be2,3]. For $d=1$ it is the Tamarkin $Δ$-colored 2-operad $\mathbf{seq}$, playing an important role in his paper [T3] and in the solution loc.cit. to the Deligne conjecture for Hochschild cochains. We expect that for hig…

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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…

An introduction to representations of p-adic groups
Jessica Fintzen
https://arxiv.org/abs/2510.08692 https://arxiv.org/pdf/2510.08692

An introduction to representations of p-adic groups
An explicit understanding of the (category of all smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and, in particular, it enables progress on various different forms of the Langlands program. In this write-up of the author's ECM 2024 colloquium-style talk, we will introduce p-adic groups and explain how the category of representations of p-adic groups decomposes into sub…

Universal properties of Delannoy categories
Kevin Coulembier, Nate Harman, Andrew Snowden
https://arxiv.org/abs/2510.10317 https://arxiv.org/pdf/2510.10317…

Universal properties of Delannoy categories
Recently, the second and third authors introduced a new symmetric tensor category $\underline{\mathrm{Perm}}(G, μ)$ associated to an oligomorphic group $G$ with a measure $μ$. When $G$ is the group of order preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semi-simple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four …

Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry
Javier Guti\'errez Garc\'ia, Ulrich H\"ohle
https://arxiv.org/abs/2510.10162 https://

Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories and whose morphisms are left adjoint distributors admits an (epi, extremal mono)--factorization system. Furthermore, we prove that the category of cocomplete quantaloid-enriched categories satisfies the weak subobject classifier axiom, under stability conditio…

Weak Hopf algebra actions as fusion category actions
Alexander Betz
https://arxiv.org/abs/2510.07114 https://arxiv.org/pdf/2510.07114

Weak Hopf algebra actions as fusion category actions
This article develops the theory of fusion categories acting on algebras. We will demonstrate that weak Hopf algebra actions on algebras correspond to specific actions of fusion categories. As an application of this theory, we introduce a family of filtered actions of weak Hopf algebras on the path algebra, and for weak Hopf algebras whose representation categories are equivalent to $\text{PSU(2)}_{p-2}$, we describe all of the separable based fusion category actions in terms of weak Hopf algeb…

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]:
- On the straightening of every functor
Thomas Blom
https://

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Homological epimorphisms in functor categories and singularity categories
Juan Andr\'es Orozco Guti\'errez, Valente Santiago Vargas

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.

An Enriched Approach to the Strictification of $(\infty,1)$-Categories
Kimball Strong
https://arxiv.org/abs/2510.04254 https://arxiv.org/pdf/2510.04254

An Enriched Approach to the Strictification of $(\infty,1)$-Categories
We define a functor which takes in an $(\infty,1)$-category and outputs an $(ω,1)$-category, the natural maximally "strict" version of an $(\infty,1)$-category. We do this by modeling $(\infty,1)$-categories as categories enriched in $\infty$-groupoids, and then "locally strictifying" (applying the strictification of $\infty$-groupoids to each hom space) to obtain a category enriched in $ω$-groupoids with respect to the Gray tensor product, followed by "globally strictifying" (strictifying th…

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…

Semisimple module categories with fusion rules of the compact full flag manifold type
Mao Hoshino
https://arxiv.org/abs/2510.12057 https://arxiv.org/pdf/25…

Semisimple module categories with fusion rules of the compact full flag manifold type
We classify semisimple left module categories over the representation category of a type A quantum group whose fusion rules arise from the maximal torus. The classification is connected to equivariant Poisson structures on compact full flag manifolds in the operator-algebraic setting, and on semisimple coadjoint orbits in the algebraic setting. We also provide an explicit construction based on the BGG categories of deformed quantum enveloping algebras, whose unitarizability corresponds to being…

Instances of models of double-categorical theories
Kevin Carlson, Evan Patterson
https://arxiv.org/abs/2510.08861 https://arxiv.org/pdf/2510.08861

Instances of models of double-categorical theories
We contribute a chapter in common to categorical database theory and to the study of higher morphisms between double categories. The common thread here is the notion of instance, or right module, which we generalize from functors from a plain category into Set to the models of a (cartesian) double theory. This provides a concept of instance for such objects as a category equipped with a monad, or a (symmetric) multicategory, recovering the multifunctors into Set in the latter case. We also show…

Unitary representations attached to parabolic subgroups: the case of abelian unipotent radical
Dan Ciubotaru
https://arxiv.org/abs/2510.11862 https://arxiv…

Unitary representations attached to parabolic subgroups: the case of abelian unipotent radical
We classify the unitary representations with integral infinitesimal character in Lusztig's category of unipotent representations in the case when the geometric parameter space comes from the action of a Levi subgroup on the abelian nilradical of a (maximal) parabolic subalgebra. We organise the unitary representations into microlocal Arthur packets. This is a test case for investigating a conjectural description of unitary representations with integral infinitesimal character.

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]:
- Measure theory via Locales
Georg Lehner
https://arxi…

[2025-10-15 Wed (UTC), 2 new articles found for math.CT Category Theory]
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An algebra modality admitting countably many deriving transformations
Jean-Baptiste Vienney
https://arxiv.org/abs/2510.03953 https://arxiv.org/pdf/2510.039…

An algebra modality admitting countably many deriving transformations
A differential category is an additive symmetric monoidal category, that is, a symmetric monoidal category enriched over commutative monoids, with an algebra modality, axiomatizing smooth functions, and a deriving transformation on this algebra modality, axiomatizing differentiation. Lemay proved that a comonoidal algebra modality has at most one deriving transformation, thus differentiation is unique in models of differential linear logic. It was then an open problem whether this result extend…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Representing the language of a topos as quotient of the category of spans
M. Golshani, A. Shiralinasab Langari

[2025-10-14 Tue (UTC), 5 new articles found for math.CT Category Theory]
toXiv_bot_toot

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Homotopy type theory as a language for diagrams of $\infty$-logoses
Taichi Uemura

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- TASI Lectures On Topological Field Theories And Differential Cohomology
Gregory W. Moore, Vivek Saxena

[2025-10-13 Mon (UTC), 1 new article found for math.CT Category Theory]
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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.

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

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}\…

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.

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Strict Rezk completions of models of HoTT and homotopy canonicity
Rafa\"el Bocquet

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Hopf bimodules for bialgebroids
Sophie Chemla, Niels Kowalzig
https://

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…