Tootfinder

I've been remiss in posting Toy Camera photos but I've added some new ones!
➡️ http://photos.rasterweb.net/index.php?/category/33
#ShittyCameraChallenge…

from my link log —
Hask is not a category.
https://math.andrej.com/2016/08/06/hask-is-not-a-category/
saved 2025-06-22

Looking for reading recommendations for your Northern Hemisphere's summer break? Our Library section can help.
https://deprogrammaticaipsum.com/category/library/

On combinatorial aspects of fat Delta
Sti\'ephen Pradal
https://arxiv.org/abs/2506.01717 https://arxiv.org/pdf/2506.01717

On combinatorial aspects of fat Delta
The category fat Delta, introduced by J. Kock, is a modification of the simplex category where the degeneracies behave weakly. The objective of this note is to provide tools for working with fat Delta. In particular, we identify three types of morphisms: degenerated, standard and vertical faces, and establish six relations between these classes. We then show that fat Delta is generated by these morphisms and relations.

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.

ProxAnn: Use-Oriented Evaluations of Topic Models and Document Clustering
Alexander Hoyle, Lorena Calvo-Bartolom\'e, Jordan Boyd-Graber, Philip Resnik
https://arxiv.org/abs/2507.00828

ProxAnn: Use-Oriented Evaluations of Topic Models and Document Clustering
Topic model and document-clustering evaluations either use automated metrics that align poorly with human preferences or require expert labels that are intractable to scale. We design a scalable human evaluation protocol and a corresponding automated approximation that reflect practitioners' real-world usage of models. Annotators -- or an LLM-based proxy -- review text items assigned to a topic or cluster, infer a category for the group, then apply that category to other documents. Using this p…

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…

The hackathon FIRSTCON25 takes place physically at 37th ANNUAL FIRST CONFERENCE on Sunday 22nd June in Copenhagen.
GCVE.eu topic has been added to the hackathon.
🔗 About the hackathon https://discourse.ossbase.org/c/hackathon-firstcon25/12
🔗 GCVE.eu topic

hackathon@FIRSTCON25
FIRST is the global Forum of Incident Response and Security Teams and this category is for the hackathon at FIRSTCON25

GOP tax bill includes a $6,000 ‘senior deduction.’ Here’s who qualifies.
Under current law, most taxpayers claim the standard deduction of $15,000 (or $30,000 for couples)
to reduce their tax liability,
though the GOP tax bill would increase those amounts slightly.
Additionally, seniors already qualify for an additional deduction of $2,000 (or $3,600 for couples).

The Senate bill would create a third category that gives seniors an additional $6,000 (or $12,000) off…

GOP tax bill includes a $6,000 ‘senior deduction.’ Here’s who qualifies.
The provision emerged from President Donald Trump’s campaign pledge to end taxes on Social Security. But experts say many are excluded.

Driving factors of auditory category learning success
Nan Wang, Gangyi Feng
https://arxiv.org/abs/2506.01508 https://arxiv.org/pdf/25…

Driving factors of auditory category learning success
Our brain learns to update its mental model of the environment by abstracting sensory experiences for adaptation and survival. Learning to categorize sounds is one essential abstracting process for high-level human cognition, such as speech perception, but it is also challenging due to the variable nature of auditory signals and their dynamic contexts. To overcome these learning challenges and enhance learner performance, it is essential to identify the impact of learning-related factors in dev…

Some functors preserving exceptionality
Dajun Liu, Hanpeng Gao, Yu-Zhe Liu
https://arxiv.org/abs/2506.00122 https://arxiv.org/pdf/250…

Some functors preserving exceptionality
We constructed some tensor functors that send each exceptional sequence in a module category to another exceptional sequence in another module category by using split extensions and recollements.

The Rouquier dimension of the category of perfect complexes over a regular ring
Janina C. Letz
https://arxiv.org/abs/2506.24038 https://

The Rouquier dimension of the category of perfect complexes over a regular ring
We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not known in general. In particular, for regular local rings this result is new. More generally, we show that a lower bound of the Rouquier dimension is given by the maximal length of a regular sequence.

Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves
R\'emi Delloque
https://arxiv.org/abs/2506.21939 https://

Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves
In this short note, we give a wide class of examples of stability conditions on the category of coherent sheaves which generalise Gieseker stability. They are referred to as "adapted to coherent sheaves" and they admit Harder-Narasimhan and Jordan-Hölder filtrations. We also study the particular case of Bayer's polynomial Bridgeland stability conditions, and their relation to the gauge theoretical counterpart introduced by Dervan-McCarthy-Sektnan.

A model structure on the category of A$_\infty$-categories with strict morphisms
Mattia Ornaghi
https://arxiv.org/abs/2506.22847 https://

A model structure on the category of A$_\infty$-categories with strict morphisms
We prove that the category of (strictly unital) A$_\infty$-categories, linear over a commutative ring $R$, with strict A$_\infty$-morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the cofibrant objects have cofibrant morphisms. As a consequence we prove that the semi-free A$_\infty$-categories (resp. resolutions) are cofibrant objects (resp. resolution) in this model structure.

On morphisms of topological quivers
Mariusz Tobolski
https://arxiv.org/abs/2506.23913 https://arxiv.org/pdf/2506.23913

On morphisms of topological quivers
We introduce regular morphisms of topological quivers and show that they give rise to a subcategory of the category of topological quivers and quiver morphisms. Our regularity conditions render the topological quiver C*-algebra construction a contravariant functor from the category of topological quivers and regular morphisms into the category of C*-algebras and $*$-homomorphisms.

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…

Advancing Lung Disease Diagnosis in 3D CT Scans
Qingqiu Li, Runtian Yuan, Junlin Hou, Jilan Xu, Yuejie Zhang, Rui Feng, Hao Chen
https://arxiv.org/abs/2507.00993

Advancing Lung Disease Diagnosis in 3D CT Scans
To enable more accurate diagnosis of lung disease in chest CT scans, we propose a straightforward yet effective model. Firstly, we analyze the characteristics of 3D CT scans and remove non-lung regions, which helps the model focus on lesion-related areas and reduces computational cost. We adopt ResNeSt50 as a strong feature extractor, and use a weighted cross-entropy loss to mitigate class imbalance, especially for the underrepresented squamous cell carcinoma category. Our model achieves a Macr…

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.

On the Definition of Intelligence
Kei-Sing Ng
https://arxiv.org/abs/2507.22423 https://arxiv.org/pdf/2507.22423

On the Definition of Intelligence
To engineer AGI, we should first capture the essence of intelligence in a species-agnostic form that can be evaluated, while being sufficiently general to encompass diverse paradigms of intelligent behavior, including reinforcement learning, generative models, classification, analogical reasoning, and goal-directed decision-making. We propose a general criterion based on sample fidelity: intelligence is the ability, given sample(s) from a category, to generate sample(s) from the same category. …

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
Yimin Huang, Zhongkai Mi, Tiancheng Qi, Quanshui Wu
https://arxiv.org/abs/2506.21879

Chevalley property and discriminant ideals of Cayley-Hamilton Hopf Algebras
For any affine Hopf algebra $H$ which admits a large central Hopf subalgebra, $H$ can be endowed with a Cayley-Hamilton Hopf algebra structure in the sense of De Concini-Procesi-Reshetikhin-Rosso. The category of finite-dimensional modules over any fiber algebra of $H$ is proved to be an indecomposable exact module category over the tensor category of finite-dimensional modules over the identity fiber algebra $H/\mathfrak{m}_{\overline{\varepsilon}}H$ of $H$. For any affine Cayley-Hamilton Hopf…

Catalan number sequences and generalized action graphs
Drew Caldwell, Ali Cochran, Nathan Glisson, Bryce Jennings, Katy McDicken, Luke Proctor, Sarah Klanderman, Amelia Tebbe
https://arxiv.org/abs/2507.22719

Catalan number sequences and generalized action graphs
Action graphs emerged from work of Bergner and Hackney on category actions in the context of Reedy categories. Alvarez, Bergner, and Lopez showed that action graphs could be inductively generated without reference to category actions and have a close relationship with the sequence of Catalan numbers. These graphs were further generalized in work of Cressman, Lin, Nguyen, and Wiljanen, who showed that the Fuss-Catalan numbers have a similar relation to another set of inductively defined directed…

Rigid Algebras and Cospans
Leor Neuhauser
https://arxiv.org/abs/2506.22072 https://arxiv.org/pdf/2506.22072

Rigid Algebras and Cospans
We introduce rigid algebras, a generalization of rigid categories to arbitrary symmetric monoidal $(\infty,2)$-categories. We develop their general theory, showing in particular that the a priori $(\infty,2)$-category of rigid algebras is in fact an $(\infty,1)$-category. For the $(\infty,2)$-category of cospans in an $(\infty,1)$-category $\mathcal{C}$, we show that the $(\infty,1)$-category of rigid commutative algebras is canonically identified with $\mathcal{C}$. This identification is used…

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…

A Diagrammatic Calculus for a Functional Model of Natural Language Semantics
Matthieu Pierre Boyer
https://arxiv.org/abs/2507.00782 https://

A Diagrammatic Calculus for a Functional Model of Natural Language Semantics
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressivity of a more traditional denotation style. We will formalize a category based type and effect system, and construct a diagrammatic calculus to model parsing and handling of effects, and use it to efficiently compute the denotations for sentences.

Order in Partial Markov Categories
Elena Di Lavore, Mario Rom\'an, Pawe{\l} Soboci\'nski, M\'ark Sz\'eles
https://arxiv.org/abs/2507.19424 https://

Order in Partial Markov Categories
Partial Markov categories are a recent framework for categorical probability theory, providing an abstract account of partial probabilistic computation. In this article, we discuss two order relations on the morphisms of a partial Markov category. In particular, we prove that every partial Markov category is canonically enriched over the category of preordered sets and monotone maps. We show that our construction recovers several well-known order enrichments. We also demonstrate that the existe…

Well, the weather forecast now includes "possible wildfires." If you go out in those wildfires, drink a lot of water and don't forget your bowler hat ->
Адска жега днес - Новини СЕГА
https://www.segabg.com/hot/category-bulgaria/adska-zhega-dnes…

Адска жега днес - Новини СЕГА
Пикът на горещата вълна от последните няколко дни се очаква да бъде днес. Червен код е издаден за областите Видин, Монтана, Враца, Плевен, Ловеч, Велико Търново, Русе, Ямбол, Хасково, Стара Загора, Пловдив, Благоевград. Там температурите ще прехвърлят 41 градуса.

The Outstanding Talk Series Emmy category will have only three nominations in 2025, down from five in 2023, due to getting just 13 submissions (Peter White/Deadline)
https://deadline.com/2025/06/late-night-talk-emmy-category-three-nominatio…

Late-Night Talk Emmy Category Reduced To Three Nominations
The likes of Jon Stewart, Stephen Colbert, Jimmy Kimmel and Seth Meyers will be battling it out for one of only three Emmy nominations.

Internet exploitation and abuse of children is a unique category of online crime and therefore cannot be used lightly by any side in debates around regulation of online privacy tools.
https://theprivacydad.com/privacy-tools-vs-online-child-exploitation-and-abu…

Modular fixed points in equivariant homotopy theory
Yorick Fuhrmann
https://arxiv.org/abs/2506.21413 https://arxiv.org/pdf/2506.21413…

Modular fixed points in equivariant homotopy theory
We show that the derived $\infty$-category of permutation modules is equivalent to the category of modules over the Eilenberg-MacLane spectrum associated to a constant Mackey functor in the $\infty$-category of equivariant spectra. On such module categories we define a modular fixed point functor using geometric fixed points followed by an extension of scalars and identify it with the modular fixed point functor on derived permutation modules introduced by Balmer-Gallauer. As an application, we…

Degenerations of maps to projective spaces
Eduardo Esteves, Piere Rodriguez, Eduardo Vital
https://arxiv.org/abs/2507.00901 https://a…

Degenerations of maps to projective spaces
Degenerations of linear series on smooth projective varieties approaching multicomponent varieties $X$ give rise to certain quiver representations in the category of linear series over $X$, which yield rational maps from $X$ to the corresponding quiver Grassmannians of codimension 1 subspaces. We describe these quiver Grassmannians for the case of the simplest quiver, arising when $X$ has only two components. We prove that they are reduced, local complete intersections whose components are rati…

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.

Archaea Exchange review https://www.soundonsound.com/reviews/archaea-exchange?u…

Berlin-based Synthflow, a no-code service letting enterprises build and deploy customized voice AI customer service agents, raised a $20M Series A led by Accel (Rebecca Szkutak/TechCrunch)
https://techcrunch.com/2025/06/24/how-

How Synthflow AI is cutting through the noise in a loud AI voice category | TechCrunch
Synthflow AI was founded in 2023 and has amassed more than 1,000 customers and handled more than 45 million calls.

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Categorical Lyapunov Theory I: Stability of Flows
Aaron D. Ames, Joe Moeller, Paulo Tabuada

Palantir not signed up for the new US health data system?
https://www.cms.gov/health-tech-ecosystem/early-adopters/data-networks

Extension category algebras and LHS--spectral sequences
Mawei Wu
https://arxiv.org/abs/2507.20588 https://arxiv.org/pdf/2507.20588

Extension category algebras and LHS--spectral sequences
Let $\mathcal{C}$ be a small category, $\mathfrak{A}$ be a precosheaf of unital $k$-algebras on $\mathcal{C}$ and $\mathfrak{M}$ be an $\mathfrak{A}$-bimodule. We introduce two new notions, namely, the Grothendieck construction $Gr_{\mathcal{C}}(\mathfrak{A}, \mathfrak{M})$ of $\mathfrak{A}$ and $\mathfrak{M}$, as well as the extension category algebra $\mathfrak{A} \ltimes \mathfrak{M}$. The extension category algebra contains the trivial extension algebra and the skew category algebra as spec…

Continual Generalized Category Discovery: Learning and Forgetting from a Bayesian Perspective
Hao Dai, Jagmohan Chauhan
https://arxiv.org/abs/2507.17382 ht…

Continual Generalized Category Discovery: Learning and Forgetting from a Bayesian Perspective
Continual Generalized Category Discovery (C-GCD) faces a critical challenge: incrementally learning new classes from unlabeled data streams while preserving knowledge of old classes. Existing methods struggle with catastrophic forgetting, especially when unlabeled data mixes known and novel categories. We address this by analyzing C-GCD's forgetting dynamics through a Bayesian lens, revealing that covariance misalignment between old and new classes drives performance degradation. Building on th…

A Markovian Approach for Cross-Category Complementarity in Choice Modeling
Omar El Housni, Shuo Sun, Rajan Udwani
https://arxiv.org/abs/2508.18566 https://…

A Markovian Approach for Cross-Category Complementarity in Choice Modeling
While single-purchase choice models have been widely studied in assortment optimization, customers in modern retail and e-commerce environments often purchase multiple items across distinct product categories, exhibiting both substitution and complementarity. We consider the cross-category assortment optimization problem where retailers jointly determine assortments across categories to maximize expected revenue. Most prior work on the topic either overlooks complementarity or proposes models t…

:neodog_base_with_nose:

Passive Vibration Isolation Characteristics of Negative Extensibility Metamaterials
Somya Ranjan Patro, Hemant Sharma, Seokgyu Yang, Jinkyu Yang
https://arxiv.org/abs/2507.00396

Passive Vibration Isolation Characteristics of Negative Extensibility Metamaterials
Negative extensibility refers to the category of mechanical metamaterials having an unusual phenomenon where the system contracts upon expansion. The dynamic analysis of such systems is crucial for exploring the vibration isolation characteristics, forming the prime focus of the present study. Inspired by the Braess paradox, the mechanical model incorporates coupled tunable nonlinear spring stiffness properties (strain hardening and softening), which alternate when a certain displacement thresh…

A Chimera domain decomposition method with weak Dirichlet-Robin coupling for finite element simulation of particulate flows
Raphael M\"unster, Otto Mierka, Dmitri Kuzmin, Stefan Turek
https://arxiv.org/abs/2506.22831

A Chimera domain decomposition method with weak Dirichlet-Robin coupling for finite element simulation of particulate flows
We introduce a new multimesh finite element method for direct numerical simulation of incompressible particulate flows. The proposed approach falls into the category of overlapping domain decomposition / Chimera / overset grid meshes. In addition to calculating the velocity and pressure of the fictitious fluid on a fixed background mesh, we solve the incompressible Navier-Stokes equations on body-fitted submeshes that are attached to moving particles. The submesh velocity and pressure are used …

Китайский классический роман "Троецарствие" невозможно читать, не обращаясь время от времени к базе данных персонажей. Их там почти тысяча.
Для сравнения, в "Войне и мире" их "всего" 559.
https://kongming.net/encyclopedia/directory/Novel

PCR-CA: Parallel Codebook Representations with Contrastive Alignment for Multiple-Category App Recommendation
Bin Tan, Wangyao Ge, Yidi Wang, Xin Liu, Jeff Burtoft, Hao Fan, Hui Wang
https://arxiv.org/abs/2508.18166

PCR-CA: Parallel Codebook Representations with Contrastive Alignment for Multiple-Category App Recommendation
Modern app store recommender systems struggle with multiple-category apps, as traditional taxonomies fail to capture overlapping semantics, leading to suboptimal personalization. We propose PCR-CA (Parallel Codebook Representations with Contrastive Alignment), an end-to-end framework for improved CTR prediction. PCR-CA first extracts compact multimodal embeddings from app text, then introduces a Parallel Codebook VQ-AE module that learns discrete semantic representations across multiple codeboo…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Coslice Colimits in Homotopy Type Theory
Perry Hart (Favonia), Kuen-Bang Hou (Favonia)

Moduli of Multi-Uniformized Stacks and Seifert $\mathbb{G}_m^d$-Bundles
Zhengkai Pan
https://arxiv.org/abs/2506.22573 https://arxiv.o…

Moduli of Multi-Uniformized Stacks and Seifert $\mathbb{G}_m^d$-Bundles
We introduce multi-uniformized stacks as a generalization of the Abramovich--Hassett construction of uniformized twisted varieties. We prove an equivalence between the category of multi $\mathbb{Q}$-line bundles satisfying an analogue of Kollár's condition and the category of multi-uniformized twisted varieties, and we construct the corresponding moduli space. We then broaden the framework to encompass Kollár's Seifert $\mathbb{G}_m^d$-bundles, showing that their moduli likewise coincide with…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Deformations of objects in $n$-categories
Fei Yu Chen
h…

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…

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.

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…

Representation theory of hereditary artin algebras of finite representation type
Shiping Liu, Gordana Todorov
https://arxiv.org/abs/2506.22987 https://

Representation theory of hereditary artin algebras of finite representation type
Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely generated left $H$-modules. This enables us to obtain an effective method to construct $\GaH$ by simply viewing the ext-quiver of $H$. As easy applications, we compute the numbers of non-isomorphic indecomposable objects in $\mmod H$ and the associated cluster category $\mathscr{C}_H$, as well as the nilpotencies of the…

ARCH-COMP25 Category Report: Stochastic Models
Alessandro Abate, Omid Akbarzadeh, Henk A. P. Blom, Sofie Haesaert, Sina Hassani, Abolfazl Lavaei, Frederik Baymler Mathiesen, Rahul Misra, Amy Nejati, Mathis Niehage, Fie {\O}rum, Anne Remke, Behrad Samari, Ruohan Wang, Rafal Wisniewski, Ben Wooding, Mahdieh Zaker
https://arxiv.org…

ARCH-COMP25 Category Report: Stochastic Models
This report is concerned with a friendly competition for formal verification and policy synthesis of stochastic models. The main goal of the report is to introduce new benchmarks and their properties within this category and recommend next steps toward next year's edition of the competition. In particular, this report introduces three recently developed software tools, a new water distribution network benchmark, and a collection of simplified benchmarks intended to facilitate further comparison…

$ 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…

On the graded singularity category of Abelian quotient singularities, I. Smooth categorical compactification
Xiaojun Chen, Jieheng Zeng
https://arxiv.org/abs/2507.19815 https://…

On the graded singularity category of Abelian quotient singularities, I. Smooth categorical compactification
Given a singularity which is the quotient of an affine space $V$ by a finite Abelian group $G \subseteq \mathrm{SL}(V)$, we study the DG enhancement $\mathcal{D}^{b}(\mathrm{tails}(k[V]^G))$ of the bounded derived category of the non-commutative projective space $\mathrm{tails}(k[V]^G)$ and the DG enhancement $\mathcal{D}_{sg}^{\mathbb{Z}}(k[V]^G)$ of its graded singularity category. In this paper, we construct smooth categorical compactifications, in the sense of Efimov, of $\mathcal{D}^b(\mat…

[2025-09-02 Tue (UTC), no new articles found for math.CT Category Theory]
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Cochain valued TQFTs from nonsemisimple modular tensor categories
Agustina Czenky, Cris Negron
https://arxiv.org/abs/2507.17169 https://arxiv.org/pdf/2507.…

Cochain valued TQFTs from nonsemisimple modular tensor categories
We show that a vector space valued TQFT constructed in work of De Renzi et al. [DGGPR23] extends naturally to a topological field theory which takes values in the symmetric monoidal category of linear cochains. Specifically, we consider a bordism category whose objects are surfaces with markings from the category of cochains Ch(A) over a given modular tensor category (such as the category of small quantum group representations), and whose morphisms are 3-dimensional bordisms with embedded ribbo…

[2025-07-02 Wed (UTC), 2 new articles found for math.CT Category Theory]
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Stabilization of the Spread-Global Dimension
Benjamin Blanchette, Justin Desrochers, Eric J. Hanson, Luis Scoccola
https://arxiv.org/abs/2506.01828 https:/…

Stabilization of the Spread-Global Dimension
Motivated by constructions from applied topology, there has been recent interest in the homological algebra of linear representations of posets, specifically in homological algebra relative to non-standard exact structures. A prominent example of such exact structure is the spread exact structure, which is an exact structure on the category of representations of a fixed poset whose indecomposable projectives are the spread representations (that is, the indicator representations of convex and co…

[2025-07-03 Thu (UTC), 2 new articles found for math.CT Category Theory]
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On Effective Banach-Mazur Games and an application to the Poincar\'e Recurrence Theorem for Category
Prajval Koul, Satyadev Nandakumar
https://arxiv.org/abs/2506.11118

On Effective Banach-Mazur Games and an application to the Poincaré Recurrence Theorem for Category
The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a proof for the effective Banach Category Theorem. Further, we provide a game-theoretic proof of an effective theorem in dynamical systems, namely the category version of Poincaré Recurrence. The Poincaré Recurrence Theorem for category states that for a hom…

[2025-06-03 Tue (UTC), 4 new articles found for math.CT Category Theory]
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Scott's Representation Theorem and the Univalent Karoubi Envelope
Arnoud van der Leer, Kobe Wullaert, Benedikt Ahrens
https://arxiv.org/abs/2506.22196 …

Scott's Representation Theorem and the Univalent Karoubi Envelope
Lambek and Scott constructed a correspondence between simply-typed lambda calculi and Cartesian closed categories. Scott's Representation Theorem is a cousin to this result for untyped lambda calculi. It states that every untyped lambda calculus arises from a reflexive object in some category. We present a formalization of Scott's Representation Theorem in univalent foundations, in the (Rocq-)UniMath library. Specifically, we implement two proofs of that theorem, one by Scott and one by Hyland.…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Antonio Ceres, Cristina Costoya, Antonio Viruel
https://arxiv.org/abs/2506.01501 https:/…

Refining Yoneda Lemma under Finiteness Constrains and Applications
Classical Yoneda Lemma asserts that the isomorphism type of an object $a$ in a category $C$ is determined by the natural type of the set-valued functor $Hom_C(a,-)$. Here we show that if finiteness hypothesis are assumed to hold in $C$, then the isomorphism type of an object $a$ in $C$ is determined by the integer-valued function $|Hom_C(a,-)|$ on objects in $C$. We present applications of this result to the isomorphism problem in Group, Graph, and Ring Theory.

A pair of monads in Topology
Ando Razafindrakoto
https://arxiv.org/abs/2507.23403 https://arxiv.org/pdf/2507.23403

A pair of monads in Topology
In the article \cite{Sim}, H. Simmons describes two monads of interests arising from the dual adjunction between the category of topological spaces and that of (bounded) distributive lattices. These are the open prime filter monad and the ideal lattice monad. It is known that the ideal lattice monad induces the ideal frame comonad on the category of frames. We show that this ideal frame comonad can be paired with the open prime filter monad via the open set-spectrum adjunction. From this, we gi…

Generating systems, generalized Thomsen collections and derived categories of toric varieties
Xiaodong Yi
https://arxiv.org/abs/2506.23531 https://

Generating systems, generalized Thomsen collections and derived categories of toric varieties
Bondal claims that for a smooth toric variety $X$, its bounded derived category of coherent sheaves $D_{c}^{b}(X)$ is generated by the Thomsen collection $T(X)$ of line bundles obtained as direct summands of the pushforward of $\mathcal{O}_{X}$ along a Frobenius map with sufficiently divisible degree. The claim is confirmed recently. In this article, we consider a generalized Thomsen collection of line bundles $T(X,D)$ with a $\mathbb{Q}$-divisor $D$ as an auxiliary input, and we prove $T(X,D)$…

De Morgan's law in toposes I
Olivia Caramello, Yorgo Chamoun
https://arxiv.org/abs/2507.01869 https://arxiv.org/pdf/2507.01869

De Morgan's law in toposes I
We study toposes satisfying De Morgan's law, in particular we give characterizations of geometric theories whose classifying topos is De Morgan, clarifying the link with the amalgamation property of the category of models of such theory. We then give several ways of turning a topos into a De Morgan topos.

Semi-strictification of $(\infty, n)$-categories
Cl\'emence Chanavat, Amar Hadzihasanovic
https://arxiv.org/abs/2507.00146 https://

Semi-strictification of $(\infty, n)$-categories
We prove the first equivalence between a weak non-algebraic model and a semi-strict algebraic model of $(\infty, n)$-categories. This takes the form of a natural semi-strictification, whereby a weak $(\infty, n)$-category is embedded into a semi-strict one through an acyclic cofibration, in such a way that weak functors lift to semi-strict functors; this constitutes the derived unit of a Quillen equivalence between weak model categories whose fibrant objects are, respectively, the weak $(\infty…

Representation stability for moduli spaces of admissible covers
Megan Chang-Lee, Siddarth Kannan, Philip Tosteson
https://arxiv.org/abs/2506.22640 https://…

Representation stability for moduli spaces of admissible covers
We prove a representation stability result for the sequence of spaces $\overline M_{g, n}^A$ of pointed admissible $A$-covers of stable $n$-pointed genus-$g$ curves, for an abelian group $A$. For fixed genus $g$ and homology degree $i$, we give the sequence of rational homology groups $H_i(\overline{M}_{g, n}^A;\mathbb Q)$ the structure of a module over a combinatorial category, a la Sam--Snowden, and prove that this module is generated in degree at most $g + 5 i$. This implies that the generat…

The NilHecke schober
Jasper van de Kreeke
https://arxiv.org/abs/2508.21737 https://arxiv.org/pdf/2508.21737

The NilHecke schober
Perverse schobers can be used to describe Fukaya categories but are hard to axiomatize and construct. In this paper, we give an explicit construction of a perverse schober intended to accurately describe the Fukaya category of the horizontal Hilbert scheme considered by Aganagic et al. in the frame of the knot invariant categorification program. The formalism is based on the notion of $ A_n $-schobers of Dyckerhoff and Wedrich. The construction is entirely algebraic and we check the schober axi…

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…

The Fano of lines, the Kuznetsov component, and a flop
Kimoi Kemboi, Ed Segal
https://arxiv.org/abs/2506.20559 https://arxiv.org/pdf/…

The Fano of lines, the Kuznetsov component, and a flop
The Kuznetsov component of the derived category of a cubic fourfold is a `non-commutative K3 surface'. Its symmetric square is hence a `non-commutative hyperkaehler fourfold'. We prove that this category is equivalent to the derived category of an actual hyperkaehler fourfold: the Fano of lines in the cubic. This verifies a conjecture of Galkin. One of the key steps in our proof is a new derived equivalence for a specific 12-dimensional flop.

Gorenstein categories and separable equivalences
Guoqiang Zhao, Juxiang Sun
https://arxiv.org/abs/2506.23243 https://arxiv.org/pdf/25…

Gorenstein categories and separable equivalences
Let $\mathscr{C}$ be an additive subcategory of left $Λ$-modules, we establish relations of the orthogonal classes of $\mathscr{C}$ and (co)res $\widetilde{\mathscr{C}}$ under separable equivalences. As applications, we obtain that the (one-sided) Gorenstein category and Wakamatsu tilting module are preserved under separable equivalences. Furthermore, we discuss when $G_{C}$-projective (injective) modules and Auslander (Bass) class with respect to $C$ are invariant under separable equivalences.

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Fra\"iss\'e limit and Ramsey Theorem: the case of MV-algebras and a categorical generalization
Ciro Russo

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Quantitative Monoidal Algebra: Axiomatising Distance with String Diagrams
Gabriele Lobbia, Wojciech R\'o\.zowski, Ralph Sarkis, Fabio Zanasi

Monomial arrow removal and the finitistic dimension conjecture
Karin Erdmann, Odysseas Giatagantzidis, Chrysostomos Psaroudakis, {\O}yvind Solberg
https://arxiv.org/abs/2506.23747

Monomial arrow removal and the finitistic dimension conjecture
In this paper, we introduce the monomial arrow removal operation for bound quiver algebras, and show that it is a novel reduction technique for determining the finiteness of the finitistic dimension. Our approach first develops a general method within the theory of abelian category cleft extensions. We then demonstrate that the specific conditions of this method are satisfied by the cleft extensions arising from strict monomial arrow removals. This crucial connection is established through the …

2-dimensional TFTs via modular $\infty$-operads
Jan Steinebrunner
https://arxiv.org/abs/2506.22104 https://arxiv.org/pdf/2506.22104…

2-dimensional TFTs via modular $\infty$-operads
This lecture series is based on joint work in progress with Shaul Barkan, as well as work in progress of the author. The five sections of these notes correspond to the five lectures, but more details have been added. $2$-dimensional topological field theories ($2$D TFTs) valued in vector spaces are commutative Frobenius algebras. The goal of this lecture series is to generalize from the $1$-category of vector spaces to any symmetric monoidal $\infty$-category $\mathcal{C}$, i.e. to study symm…

[2025-09-01 Mon (UTC), 2 new articles found for math.CT Category Theory]
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[2025-08-01 Fri (UTC), 2 new articles found for math.CT Category Theory]
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[2025-07-01 Tue (UTC), 7 new articles found for math.CT Category Theory]
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When are exact categories co-exact?
James Richard Andrew Gray
https://arxiv.org/abs/2506.23413 https://arxiv.org/pdf/2506.23413

When are exact categories co-exact?
We show that opposite category of a cocomplete pretopos is ideally exact and arithmetical. We do this by showing that there are conditions common to additive and lextensive categories which, in the exact context, imply that: pushouts of monomorphisms along arbitrary morphisms exist and are pullbacks; monomorphisms are stable under pushout; co-reflexive-relations are co-effective-equivalence-relations; and coprotomodularity holds.

Local presentability and monadicity of forgetful functors for operator algebraic categories
Alexandru Chirvasitu, Ian Thompson
https://arxiv.org/abs/2507.23152 https://

Local presentability and monadicity of forgetful functors for operator algebraic categories
In recent work of Lindenhovius and Zamdzhiev, it was established that the category of complete operator spaces, with completely contractive linear maps as morphisms, is locally countably presentable. In this work, we extend their conclusion to the non-complete setting and prove that the categories of operator systems, (Archimedean) order unit spaces, and unital operator algebras are all locally countably presentable as well. This is established through an analysis of forgetful functors and the …

Large condensation in enriched $\infty$-categories
Devon Stockall
https://arxiv.org/abs/2506.23632 https://arxiv.org/pdf/2506.23632…

Large condensation in enriched $\infty$-categories
Using the language of enriched $\infty$-categories, we formalize and generalize the definition of fusion n-category, and an analogue of iterative condensation of $E_i$-algebras. The former was introduced by Johnson-Freyd, and the latter by Kong, Zhang, Zhao, and Zheng. This extends categorical condensation beyond fusion n-categories to all enriched monoidal $\infty$-categories with certain colimits. The resulting theory is capable of treating symmetries of arbitrary dimension and codimension th…

Doubly weak double categories
Aaron David Fairbanks, Michael Shulman
https://arxiv.org/abs/2506.23651 https://arxiv.org/pdf/2506.2365…

Doubly weak double categories
We propose a definition of double categories whose composition of 1-cells is weak in both directions. Namely, a doubly weak double category is a double computad -- a structure with 2-cells of all possible double-categorical shapes -- equipped with all possible composition operations, coherently. We also characterize them using "implicit" double categories, which are double computads having all possible compositions of 2-cells, but no compositions of 1-cells; doubly weak double categories are th…

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…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Growth problems in diagram categories
Jonathan Gruber, Daniel Tubbenhauer
htt…

Hopf categories associated to comonoidal functors
Andrea Rivezzi
https://arxiv.org/abs/2506.22872 https://arxiv.org/pdf/2506.22872

Hopf categories associated to comonoidal functors
We provide an explicit construction of Hopf categories associated to comonoidal functors, generalizing Ševera's construction of Hopf monoids through M-adapted functors. We discuss the example of the Hopf category whose underlying class is the set of twists of a Lie bialgebra. Finally, we apply the result to the setting of deformed categories.

Annulation (co)homologique pour des repr\'esentations non additives d'une cat\'egorie semi-additive
Benachir El Allaoui
https://arxiv.org/abs/2507.19317 https://

Annulation (co)homologique pour des représentations non additives d'une catégorie semi-additive
We show the vanishing of higher extension groups and torsion groups between linearisation of additive functors from a semi-additive category satisfying some conditions to a category of vector spaces. In particular, we apply our results to the category of correspondences functors of Bouc-Thévenaz.

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.

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…

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://…

Morphisms and comorphisms of sites II - Distributors of sites
Axel Osmond, Olivia Caramello
https://arxiv.org/abs/2507.20932 https://arxiv.org/pdf/2507.209…

Morphisms and comorphisms of sites II - Distributors of sites
We introduce a notion of distributor of sites, involving suited analogs of flatness and cover-preservation, and show that this notion jointly generalizes those of morphism and comorphism of sites. Given two sites, we exhibit an adjunction between the category of distributors of sites between them and the category of geometric morphisms between the associated sheaf topoi; this adjunction restricts to an equivalence between geometric morphisms and continuous distributors of sites. We finally disc…

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.

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Rigidity of non-negligible objects of moderate growth in braided categories
Pavel Etingof, David Penneys

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Partially Dualized Quasi-Hopf Algebras Reconstructed from Dual Tensor Categories to Finite-Dimens...
Kangqiao Li

[2025-07-31 Thu (UTC), no new articles found for math.CT Category Theory]
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[2025-06-30 Mon (UTC), 2 new articles found for math.CT Category Theory]
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Temperley-Lieb Categories on Non-Orientable Surfaces
Dionne Ibarra, Gabriel Montoya-Vega, Benjamin Morris
https://arxiv.org/abs/2506.14319 https://

Temperley-Lieb Categories on Non-Orientable Surfaces
In this paper we present the construction of a skeletal diagram category, which we call the square with bands category. This category extends the Temperley-Lieb (TL) category, where morphisms now include diagrams of embedded curves on (possibly) non-orientable bounded surfaces, and involves three parameters associated to simple closed curves. Such diagrams utilise handle decompositions for surfaces and are considered up to a handle slide equivalence. We define a tensor product on this category,…

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Metric completions of triangulated categories from hereditary rings
Cyril Matou\v{s}ek

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- The Flat Cover Conjecture for Monoid Acts
Sean Cox
https://

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Shadows are Bicategorical Traces
Kathryn Hess, Nima Rasekh

Cofibrant generation of pure monomorphisms in presheaf categories
Sean Cox, Jonathan Feigert, Mark Kamsma, Marcos Mazari-Armida, Ji\v{r}\'i Rosick\'y
https://arxiv.org/abs/2506.20278

Cofibrant generation of pure monomorphisms in presheaf categories
We characterise when the pure monomorphisms in a presheaf category $\mathbf{Set}^\mathcal{C}$ are cofibrantly generated in terms of the category $\mathcal{C}$. In particular, when $\mathcal{C}$ is a monoid $S$ this characterises cofibrant generation of pure monomorphisms between sets with an $S$-action in terms of $S$: this happens if and only if for all $a, b \in S$ there is $c \in S$ such that $a = cb$ or $ca = b$. We give a model-theoretic proof: we prove that our characterisation is equival…