Tootfinder

Simplicial Approach to Frobenius Algebras in the Category of Relations
Dominik Lachman
https://arxiv.org/abs/2509.06193 https://arxiv.org/pdf/2509.06193

Simplicial Approach to Frobenius Algebras in the Category of Relations
Frobenius algebras in the category of sets and relations ($\mathbf{Rel}$) serve as a unifying framework for various algebraic and combinatorial structures, including groupoids, effect algebras, and abstract circles. Recently, a nerve construction of simplicial sets for Frobenius algebras in $\mathbf{Rel}$ has been introduced. In this work, we investigate the lifting properties of these simplicial sets, linking them to the algebraic properties of Frobenius algebras. We introduce $ε$-simplicial …

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 …

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.

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…

Doy por inaugurada una nueva sección en mi blog «Pixeblog», que serš el reemplazo de lo que hasta ahora hacía en Pixelfed, o sea, publicar fotos casuales de conciertos, lugares y otras cosas que considero que vale la pena ser registradas. Como esto estš federado, sigue siendo visible por acš y en Pixelfed.
🔗 https://altgr.xyz/category/pixeb…

The compact double category $\mathbf{Int}(\mathbf{Poly}_*)$ models control flow and data transformations
Grigory Kondyrev, David I. Spivak
https://arxiv.org/abs/2509.05462 https…

The compact double category $\mathbf{Int}(\mathbf{Poly}_*)$ models control flow and data transformations
Hasegawa showed that control flow in programming languages -- while loops and if-then-else statements -- can be modeled using traced cocartesian categories, such as the category $\mathbf{Set}_*$ of pointed sets. In this paper we define an operad $\mathscr{W}$ of wiring diagrams that provides syntax for categories whose control flow moreover includes data transformations, including deleting, duplicating, permuting, and applying pre-specified functions to variables. In the most basic version, the…

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…

Spectral and Rhythm Feature Performance Evaluation for Category and Class Level Audio Classification with Deep Convolutional Neural Networks
Friedrich Wolf-Monheim
https://arxiv.org/abs/2509.07756

Spectral and Rhythm Feature Performance Evaluation for Category and Class Level Audio Classification with Deep Convolutional Neural Networks
Next to decision tree and k-nearest neighbours algorithms deep convolutional neural networks (CNNs) are widely used to classify audio data in many domains like music, speech or environmental sounds. To train a specific CNN various spectral and rhythm features like mel-scaled spectrograms, mel-frequency cepstral coefficients (MFCC), cyclic tempograms, short-time Fourier transform (STFT) chromagrams, constant-Q transform (CQT) chromagrams and chroma energy normalized statistics (CENS) chromagrams…

Finished "Automatic Noodle" by Annalee Newitz, a novella comfortably ensconced in the "cozy sci-fi" category. Becky Chambers fan? This one is probably a pretty safe bet!
A group of food service robots facing an uncertain future in the aftermath of a war decides to give it a go in their own restaurant. Only they aren't technically able to own one and they face some adversity that requires them to pull together.
3.5/5 stars, rounded up ⭐ ⭐ ⭐ ⭐

Automatic Noodle
From sci-fi visionary and acclaimed author Annalee Newi…

Simple homotopy theory for Fukaya categories
Yonghwan Kim
https://arxiv.org/abs/2509.05856 https://arxiv.org/pdf/2509.05856

Simple homotopy theory for Fukaya categories
We develop a categorical framework for simple homotopy theory in Fukaya categories, based on the fundamental group of the ambient symplectic manifold. When the first Chern class vanishes, we show that any isomorphism in the Fukaya category of a Weinstein manifold has trivial Whitehead torsion. As an application, we prove that any pair of closed connected Lagrangians that are isomorphic in the Fukaya category of such Weinstein manifolds are simple homotopy equivalent, provided one of the Lagrang…

D-HUMOR: Dark Humor Understanding via Multimodal Open-ended Reasoning
Sai Kartheek Reddy Kasu, Mohammad Zia Ur Rehman, Shahid Shafi Dar, Rishi Bharat Junghare, Dhanvin Sanjay Namboodiri, Nagendra Kumar
https://arxiv.org/abs/2509.06771

D-HUMOR: Dark Humor Understanding via Multimodal Open-ended Reasoning
Dark humor in online memes poses unique challenges due to its reliance on implicit, sensitive, and culturally contextual cues. To address the lack of resources and methods for detecting dark humor in multimodal content, we introduce a novel dataset of 4,379 Reddit memes annotated for dark humor, target category (gender, mental health, violence, race, disability, and other), and a three-level intensity rating (mild, moderate, severe). Building on this resource, we propose a reasoning-augmented f…

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…

Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
Leonid Positselski
https://arxiv.org/abs/2509.07645 https://

Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
Given a hereditary complete cotorsion pair $(\mathsf A,\mathsf B)$ generated by a set of objects in a Grothendieck category $\mathsf K$, we construct a natural equivalence between the Becker coderived category of the left-hand class $\mathsf A$ and the Becker contraderived category of the right-hand class $\mathsf B$. We show that a nested pair of cotorsion pairs $(\mathsf A_1,\mathsf B_1)\le(\mathsf A_2,\mathsf B_2)$ provides an adjunction between the related co/contraderived categories, which…

Crosslisted article(s) found for cs.PL. https://arxiv.org/list/cs.PL/new
[1/1]:
- The compact double category $\mathbf{Int}(\mathbf{Poly}_*)$ models control flow and data transfor...
Grigory Kondyrev, David I. Spivak

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…

Oriented matroids and type $\mathbb{A}$ cluster categories
Nicholas J. Williams
https://arxiv.org/abs/2509.07883 https://arxiv.org/pdf/2509.07883

Oriented matroids and type $\mathbb{A}$ cluster categories
For any cluster-tilting object $\mathsf{T}$ in the cluster category $\mathscr{C}_{n}$ of type $\mathbb{A}_{n}$, we construct a rank-four oriented matroid $\mathcal{M}_{\mathsf{T}}$ such that stackable triangulations of $\mathcal{M}_{\mathsf{T}}$ are in bijection with equivalence classes of maximal green sequences with initial cluster $\mathsf{T}$. This generalises the result that equivalence classes of maximal green sequences of linearly oriented $\mathbb{A}_{n}$ are in bijection with triangula…

Bridging the Gap Between Theoretical and Practical Reinforcement Learning in Undergraduate Education
Muhammad Ahmed Atif, Mohammad Shahid Shaikh
https://arxiv.org/abs/2509.05689

Bridging the Gap Between Theoretical and Practical Reinforcement Learning in Undergraduate Education
This innovative practice category paper presents an innovative framework for teaching Reinforcement Learning (RL) at the undergraduate level. Recognizing the challenges posed by the complex theoretical foundations of the subject and the need for hands-on algorithmic practice, the proposed approach integrates traditional lectures with interactive lab-based learning. Drawing inspiration from effective pedagogical practices in computer science and engineering, the framework engages students throug…

WR Michael Pittman moves up in Colts' record book after win v. Raiders https://coltswire.usatoday.com/story/sports/nfl/colts/2025/10/08/michael-pittman-now-5th-receptions-colts-franchise-history/8658107900…

Homotopy theory of simplicial parametrized operads
Gregoire Marc
https://arxiv.org/abs/2510.06932 https://arxiv.org/pdf/2510.06932

Homotopy theory of simplicial parametrized operads
We define a generalization of (coloured) operads based on double lax functors and we construct a model structure on the associated category of generalized simplicial (coloured) operads. In particular, we obtain a model structure on the category of simplicial (coloured) O-operads of Nardin and Shah.

A Higgs category for the cluster variety of triples of flags
Bernhard Keller, Miantao Liu
https://arxiv.org/abs/2509.04863 https://arxiv.org/pdf/2509.04863…

A Higgs category for the cluster variety of triples of flags
The cluster variety of triples of flags (associated with a split simple Lie group of Dynkin type Delta) plays a key role in higher Teichmuller theory as developed by Fock-Goncharov, Jiarui Fei, Ian Le, ... and Goncharov-Shen. We refer to it as the basic triangle associated with Delta. In this paper, for simply laced Delta, we construct and study a Higgs category (in the sense of Yilin Wu) which we expect to categorify the basic triangle. This category is a certain exact dg category (in the sens…

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

SymTFT actions, Condensable algebras and Categorical anomaly resolutions
Daniel Robbins, Subham Roy
https://arxiv.org/abs/2509.05408 https://arxiv.org/pdf/…

SymTFT actions, Condensable algebras and Categorical anomaly resolutions
We investigate symmetry topological field theories (SymTFTs) of non-abelian and non-invertible symmetries and the different Lagrangian algebras associated with a given Drinfeld center. For several examples we analyze the condensable algebras of the Drinfeld center to identify the intrinsically gapless symmetry protected topological (igSPT) phases. In previous work, the relation between igSPT phases and resolving anomalies by embedding an anomalous symmetry inside a larger fusion category was de…

Classifying KE-closed subcategories over a commutative noetherian ring
Toshinori Kobayashi, Shunya Saito
https://arxiv.org/abs/2509.05767 https://arxiv.org…

Classifying KE-closed subcategories over a commutative noetherian ring
Let $\mathsf{mod} R$ denote the category of finitely generated $R$-modules for a commutative noetherian ring $R$. In this paper, we investigate KE-closed subcategories of $\mathsf{mod} R$ as a continuation of our previous work. We associate a function on $\mathrm{Spec} R$ with each KE-closed subcategory of $\mathsf{mod} R$, and show that this function completely determines the original subcategory. To classify the functions obtained from KE-closed subcategories, we introduce the notion of an $n…

Replaced article(s) found for q-bio.NC. https://arxiv.org/list/q-bio.NC/new
[1/1]:
- Language learning shapes visual category-selectivity in deep neural networks
Zitong Lu, Yuxin Wang

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

Fast phase prediction of charged polymer blends by white-box machine learning surrogates
Clayton Ellis, Xinyi Fang, Christopher Balzer, Timothy Quah, M. Scott Shell, Glenn H. Fredrickson, Mengyang Gu
https://arxiv.org/abs/2509.07164

Fast phase prediction of charged polymer blends by white-box machine learning surrogates
Compatibilized polymer blends are a complex, yet versatile and widespread category of material. When the components of a binary blend are immiscible, they are typically driven towards a macrophase-separated state, but with the introduction of electrostatic interactions, they can be either homogenized or shifted to microphase separation. However, both experimental and simulation approaches face significant challenges in efficiently exploring the vast design space of charge-compatibilized polymer…

Conjugacies of geodesic flows in affine cylinders and tori
Xavier Buff (IMT), Guillaume Tahar (BIMSA)
https://arxiv.org/abs/2509.06391 https://arxiv.org/pd…

Conjugacies of geodesic flows in affine cylinders and tori
Affine cylinders (genus zero surfaces with two singularities) and affine tori (genus one surfaces without singularities) are among the simplest examples of surfaces endowed with a complex affine structure. Their geodesic flows are particularly tractable. In this article, we provide explicit necessary and sufficient conditions under which the geodesic flows on such surfaces are conjugate, in the topological and in the holomorphic category.

Nonuniqueness for high-dimensional ideal MHD equations via differential inclusion
Changxing Miao, Zhiwen Zhao
https://arxiv.org/abs/2509.06866 https://arxi…

Nonuniqueness for high-dimensional ideal MHD equations via differential inclusion
In this paper, we establish the non-uniqueness of solutions to the ideal magnetohydrodynamics equations in any dimension greater than three by proving the existence of infinitely many compactly supported weak solutions. In particular, these solutions fail to conserve the total energy. Our proof relies on the differential inclusion framework tailored to the geometry of ideal MHD system, which enables the simultaneous use of Baire category method and convex integration scheme.

Systematic Evaluation of Multi-modal Approaches to Complex Player Profile Classification
Jason Starace, Terence Soule
https://arxiv.org/abs/2509.05624 https://

Systematic Evaluation of Multi-modal Approaches to Complex Player Profile Classification
Modern adaptive games require nuanced player understanding, yet most models use simplified 5-10 category taxonomies that fail to capture diversity. Behavioral clustering cannot distinguish players with different motivations who act similarly. We present a systematic evaluation of multi-modal classification at scale, combining behavioral telemetry with semantic context to support 36 player profiles. Using 19,413 gameplay sessions from an AI-controlled text-based RPG, we compared behavioral-only …

Equivariant Eilenberg-Watts theorems for locally compact quantum groups
Joeri De Ro
https://arxiv.org/abs/2510.06206 https://arxiv.org/pdf/2510.06206

Equivariant Eilenberg-Watts theorems for locally compact quantum groups
Given two von Neumann algebras $A$ and $B$, the $W^*$-algebraic Eilenberg-Watts theorem, due to M. Rieffel, asserts that there is a canonical equivalence $\operatorname{Corr}(A,B)\simeq \operatorname{Fun}(\operatorname{Rep}(B), \operatorname{Rep}(A))$ of categories, where $\operatorname{Corr}(A,B)$ denotes the category of all $A$-$B$-correspondences, $\operatorname{Rep}(A)$ is the category of all unital normal $*$-representations of $A$ on Hilbert spaces and $\operatorname{Fun}(\operatorname{Re…

Hawaii issues state of emergency as Hurricane Kiko approaches islands as Category 4
https://thehill.com/homenews/state-watch/5490353-hurricane-kiko-hawaii-storm/

Crosslisted article(s) found for cs.AI. https://arxiv.org/list/cs.AI/new
[15/17]:
- DiT-VTON: Diffusion Transformer Framework for Unified Multi-Category Virtual Try-On and Virtual T...
Qi Li, Shuwen Qiu, Julien Han, Xingzi Xu, Mehmet Saygin Seyfioglu, Kee Kiat Koo, Karim Bouyarmane

Very-Well-Behaved Epireflections for Categories of Models of Sketches
Jo\~ao J. Xarez
https://arxiv.org/abs/2509.07241 https://arxiv.org/pdf/2509.07241

Very-Well-Behaved Epireflections for Categories of Models of Sketches
Firstly, precise conditions on how to obtain very-well-behaved epireflections are explored and improved from the author's previous papers; meaning that, beginning with a monad and a prefactorization system on a category, is produced a reflection with stable units (stronger than semi-left-exactness, also called admissibility in categorical Galois Theory) and an associated monotone-light factorization. Then, we were able to show that, for a pseudo-filtered category J in which every arrow is a mon…

A note on cubic fourfolds containing multiple planes
Moritz Hartlieb
https://arxiv.org/abs/2509.06666 https://arxiv.org/pdf/2509.06666

A note on cubic fourfolds containing multiple planes
We study the geometry, Hodge theory and derived category of cubic fourfolds containing multiple planes and their associated twisted K3 surfaces. We focus on the case of two planes intersecting along a line.

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…

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…

Automorphisms of valued fields: amalgamation and existential closedness
Jan Dobrowolski, Francesco Gallinaro, Rosario Mennuni
https://arxiv.org/abs/2510.06021 https://

Automorphisms of valued fields: amalgamation and existential closedness
We study valued fields equipped with an automorphism. We prove that all of them have an extension admitting an equivariant cross-section of the valuation. In residual characteristic zero, and in the presence of such a cross-section, we show that amalgamation problems are solvable precisely when the induced residual problem is, characterise the existentially closed objects of this category, and prove that its positive theory does not have the tree property of the second kind. We prove analogous …

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…

One rig to control them all
Chris Heunen, Robin Kaarsgaard, Louis Lemonnier
https://arxiv.org/abs/2510.05032 https://arxiv.org/pdf/2510.05032

One rig to control them all
We introduce a theory for computational control, consisting of seven naturally interpretable equations. Adding these to a prop of base circuits constructs controlled circuits, borne out in examples of reversible Boolean circuits and quantum circuits. We prove that this syntactic construction semantically corresponds to taking the free rig category on the base prop.

Partializations of Markov categories
Areeb Shah Mohammed
https://arxiv.org/abs/2509.05094 https://arxiv.org/pdf/2509.05094…

Partializations of Markov categories
The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier models of categories of partial morphisms such as p-categories, dominical categories, restriction categories, etc. to a non-deterministic/non-cartesian setting. Here all morphisms are quasi-total, with a natural poset enrichment corresponding to one morphism being a restriction of the other. Furthermo…

I get immensely distressed when I see students building a little nest for themselves in just one proverbial corner of campus. Perhaps my most common advising conversation is “You do not need to take 3 classes at once in this department. What about <<category you’ve never studied>>?”
(Macalester is a liberal arts college, so our curriculum is carefully calibrated such that there is •room• for students to touch many disciplines. That’s the point. Yes, there are other kinds of schools where do you have to take almost all your classes in one dept. I am leery of that.)

Hopf bimodules for bialgebroids
Sophie Chemla, Niels Kowalzig
https://arxiv.org/abs/2510.06417 https://arxiv.org/pdf/2510.06417

Hopf bimodules for bialgebroids
Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in this realm. By explicitly formulating a fundamental theorem for Hopf modules via the concept of Hopf-Galois comodules, we prove that the category of Hopf bimodules can be endowed with the structure of a (pre-)braided monoidal category in two different ways, …

Geometric Construction of Quiver Tensor Products
Daigo Ito, John S. Nolan
https://arxiv.org/abs/2510.05277 https://arxiv.org/pdf/2510.05277

Geometric Construction of Quiver Tensor Products
By a classic theorem of Beilinson, the perfect derived category $\operatorname{Perf}(\mathbb{P}^n)$ of projective space is equivalent to the category of derived representations of a certain quiver with relations. The vertex-wise tensor product of quiver representations corresponds to a symmetric monoidal structure $\otimes_{\mathsf{Q}}$ on $\operatorname{Perf}(\mathbb{P}^n)$. We prove that, for a certain choice of equivalence, the symmetric monoidal structure $\otimes_{\mathsf{Q}}$ may be descr…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- LS-category and sequential topological complexity of symmetric products
Ekansh Jauhari

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

MICACL: Multi-Instance Category-Aware Contrastive Learning for Long-Tailed Dynamic Facial Expression Recognition
Feng-Qi Cui, Zhen Lin, Xinlong Rao, Anyang Tong, Shiyao Li, Fei Wang, Changlin Chen, Bin Liu
https://arxiv.org/abs/2509.04344

MICACL: Multi-Instance Category-Aware Contrastive Learning for Long-Tailed Dynamic Facial Expression Recognition
Dynamic facial expression recognition (DFER) faces significant challenges due to long-tailed category distributions and complexity of spatio-temporal feature modeling. While existing deep learning-based methods have improved DFER performance, they often fail to address these issues, resulting in severe model induction bias. To overcome these limitations, we propose a novel multi-instance learning framework called MICACL, which integrates spatio-temporal dependency modeling and long-tailed contr…

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

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

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

On numerical invariants of retraction map
Nursultan Kuanyshov
https://arxiv.org/abs/2509.05745 https://arxiv.org/pdf/2509.05745

On numerical invariants of retraction map
We introduce a notion of retraction between continuous maps of topological spaces and study the behavior of several numerical invariants under such retractions. These include (co)homological dimensions, the Lusternik-Schnirelmann category, the topological complexity, and the sequential topological complexity. We prove that, under the retraction map, the corresponding inequalities between invariants hold. Our results also apply to recent invariants are defined by Dranishnikov, Jauhari \cite{DJ} …

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

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/

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 16726 nodes and 47594 edges.
Tags: Social, Collaboratio…

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://

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

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

Annihilation of cohomology over one dimensional almost Gorenstein rings
\"Ozg\"ur Esentepe
https://arxiv.org/abs/2510.05720 https://arxiv.org/pdf…

Annihilation of cohomology over one dimensional almost Gorenstein rings
Given a Cohen-Macaulay local ring, the cohomology annihilator ideal and the annihilator of the stable category of maximal Cohen-Macaulay modules are two ideals closely related both with each other and the singularities of the ring. Kimura recently showed that the two ideals agree up to radicals. In this article, we give a sufficient condition for the two ideals to be equal. As an application, we show that the cohomology annihilator ideal of a one dimensional analytically unramified almost Goren…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Categorical semantics of compositional reinforcement learning
Georgios Bakirtzis, Michail Savvas, Ufuk Topcu

A strong finiteness condition for smashing localisations
Isabel Longbottom
https://arxiv.org/abs/2509.07344 https://arxiv.org/pdf/2509.07344

A strong finiteness condition for smashing localisations
We define a class of smashing localisations which we call compactly central, and classify compactly central localisations of $Sp_{(p)}$ and of $Sp$. Our main result is that $L_n^f$ is a compactly central localisation. A map $α: 1 \to A$ in a presentably symmetric monoidal $\infty$-category $\mathscr{C}$ is central if there exists a homotopy $α\otimes id_A \simeq id_A \otimes α: A \to A \otimes A$. A central map $α$ can be used to produce a smashing localisation $L_α$ of $\mathscr{C}$, be…

Abelian quotients of categories of $n$-exangles
Yutong Zhou
https://arxiv.org/abs/2510.06626 https://arxiv.org/pdf/2510.06626

Abelian quotients of categories of $n$-exangles
The notion of $n$-exangulated categories was introduced by Herschend-Liu-Nakaoka, which is a simultaneous generalization of $n$-exact categories in the sense of Jasso and $(n+2)$-angulated categories in the sense of Geiss-Kelier-Oppermann. Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an $n$-exangulated category with enough projectives $\mathcal{P}$ and $\mathcal{M}$ a full subcategory of $\mathscr{C}$ containing $\mathcal{P}$. In the present paper, It is proved that a certian quotient categor…

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Classification of silted algebras for two quivers of Dynkin type $\mathbb{D}_{n}$
Houjun Zhang

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- A functorial approach to $n$-abelian categories
Vitor Gulisz
https://

On syzygy categories over Iwanaga-Gorenstein algebras: Reduction, minimality and finiteness
Ralf Schiffler, Khrystyna Serhiyenko
https://arxiv.org/abs/2510.07405 https://…

On syzygy categories over Iwanaga-Gorenstein algebras: Reduction, minimality and finiteness
We study 2-Calabi-Yau tilted algebras which are non-commutative Iwanaga-Gorenstein algebras of Gorenstein dimension 1. In particular, we are interested in their syzygy categories or equivalently the stable categories of Cohen-Macauley modules $\underline{\text{CMP}}$. First we show that if an algebra $A$ is Iwanaga-Gorenstein of Gorenstein dimension 1 then its stable category is generated under extensions by its radical $\text{rad}\,A$. Next, for a 2-Calabi-Yau tilted algebra $A$ we provide an …

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…

Artin--Mazur formal groups and Milne duality via unipotent spectra
Shubhodip Mondal, Tasos Moulinos, Lucy Yang
https://arxiv.org/abs/2510.06152 https://arx…

Artin--Mazur formal groups and Milne duality via unipotent spectra
We introduce and develop the notion of "unipotent spectra." This is defined to be the stabilization of Toën's category of affine stacks, and is related to recent work of Mondal--Reinecke. Unipotent spectra give rise to unipotent stable homotopy groups and unipotent homology, which are new invariants for schemes valued in unipotent group schemes. As applications, we recover the Artin--Mazur formal groups associated to schemes without any vanishing assumptions. Further, we show that syntomic coh…

Exploiting Unlabeled Structures through Task Consistency Training for Versatile Medical Image Segmentation
Shengqian Zhu, Jiafei Wu, Xiaogang Xu, Chengrong Yu, Ying Song, Zhang Yi, Guangjun Li, Junjie Hu
https://arxiv.org/abs/2509.04732

Exploiting Unlabeled Structures through Task Consistency Training for Versatile Medical Image Segmentation
Versatile medical image segmentation (VMIS) targets the segmentation of multiple classes, while obtaining full annotations for all classes is often impractical due to the time and labor required. Leveraging partially labeled datasets (PLDs) presents a promising alternative; however, current VMIS approaches face significant class imbalance due to the unequal category distribution in PLDs. Existing methods attempt to address this by generating pseudo-full labels. Nevertheless, these typically req…

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

MCANet: A Multi-Scale Class-Specific Attention Network for Multi-Label Post-Hurricane Damage Assessment using UAV Imagery
Zhangding Liu, Neda Mohammadi, John E. Taylor
https://arxiv.org/abs/2509.04757 …

MCANet: A Multi-Scale Class-Specific Attention Network for Multi-Label Post-Hurricane Damage Assessment using UAV Imagery
Rapid and accurate post-hurricane damage assessment is vital for disaster response and recovery. Yet existing CNN-based methods struggle to capture multi-scale spatial features and to distinguish visually similar or co-occurring damage types. To address these issues, we propose MCANet, a multi-label classification framework that learns multi-scale representations and adaptively attends to spatially relevant regions for each damage category. MCANet employs a Res2Net-based hierarchical backbone t…

Window categories for a simple $9$-fold flop of Grassmannian type
Will Donovan, Wahei Hara, Micha{\l} Kapustka, Marco Rampazzo
https://arxiv.org/abs/2510.06184 https://

Window categories for a simple $9$-fold flop of Grassmannian type
The local simple $9$-fold flop of Grassmannian type is a birational transformation between total spaces of vector bundles on the Grassmannians $\mathrm{Gr}(2, 5)$ and $\mathrm{Gr}(3, 5)$. We produce four different derived equivalences which commute with the pushforward functors for the flopping contractions. These equivalences are realized by identifying four different window categories inside the derived category of coherent sheaves on an Artin stack. As an application, our approach provides a…

[2025-10-10 Fri (UTC), 2 new articles found for math.CT Category Theory]
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[2025-10-09 Thu (UTC), 2 new articles found for math.CT Category Theory]
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TEn-CATS: Text-Enriched Audio-Visual Video Parsing with Multi-Scale Category-Aware Temporal Graph
Yaru Chen, Faegheh Sardari, Peiliang Zhang, Ruohao Guo, Yang Xiang, Zhenbo Li, Wenwu Wang
https://arxiv.org/abs/2509.04086

TEn-CATS: Text-Enriched Audio-Visual Video Parsing with Multi-Scale Category-Aware Temporal Graph
Audio-Visual Video Parsing (AVVP) task aims to identify event categories and their occurrence times in a given video with weakly supervised labels. Existing methods typically fall into two categories: (i) designing enhanced architectures based on attention mechanism for better temporal modeling, and (ii) generating richer pseudo-labels to compensate for the absence of frame-level annotations. However, the first type methods treat noisy segment-level pseudo labels as reliable supervision and the…

[2025-09-09 Tue (UTC), 5 new articles found for math.CT Category Theory]
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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.

[2025-09-10 Wed (UTC), 3 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…

Concentration structures on categories and horizontal categorification
Yangxiao Luo, Shunyu Wan
https://arxiv.org/abs/2510.07553 https://arxiv.org/pdf/2510…

Concentration structures on categories and horizontal categorification
We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration structure we can functorially construct a $\textit{concentration monoid}$, which can be used to give a precise definition of horizontal categorification and decategorification. Moreover, by studying concentration structures on fundamental groupoids, we show that ev…

Two-dimensional transducers
Fosco Loregian
https://arxiv.org/abs/2509.06769 https://arxiv.org/pdf/2509.06769

Two-dimensional transducers
We define a bicategory $\mathbf{2TDX}$ whose 1-cells provide a categorification of transducers, computational devices extending finite-state automata with output capabilities. This bicategory is a mathematically interesting object: its objects are categories $\mathcal{A},\mathcal{B},\dots$ and its 1-cells $(\mathcal{Q}, t) : \mathcal{A} \to \mathcal{B}$ consist of a category $\mathcal{Q}$ of `states', and a profunctor $$ t : \mathcal{A} \times \mathcal{Q}^\text{op}\times\mathcal{Q} \times (\mat…

Categorical Tiling Theory: Constructing Directed Planar Tilings via Edge Reversal
Catherine DiLeo, Preston Sessoms, Brandon T. Shapiro
https://arxiv.org/abs/2509.06363 https://

Categorical Tiling Theory: Constructing Directed Planar Tilings via Edge Reversal
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories corresponding to polygons with labeled directed edges, and introduce the problem of modeling tilings of the Euclidean or hyperbolic plane as presheaves over such a category. Combinatorially, this amounts to choosing an ``alignment'' for a tiling: a direction for every edge and consistent labels for the edges of each polygonal t…

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…

A limit lifting theorem for fibrations between bicategories
Patrick Nicodemus
https://arxiv.org/abs/2509.04639 https://arxiv.org/pdf/2509.04639

A limit lifting theorem for fibrations between bicategories
A standard result from the theory of Grothendieck fibrations states that if $p : E \to B$ is a fibration, then $E$ has limits of shape $\mathcal{J}$ if $B$ has limits of shape $\mathcal{J}$ the fibers of $\mathcal{E}$ have limits of shape $\mathcal{J}$, and the reindexing functors preserve these limits. Such a result is a basic tool when computing limits in a category known to be the total category of a fibration, for example, one that is defined using the Grothendieck construction. This paper …

On the equivalence invariance of formal category theory
Paula Verdugo
https://arxiv.org/abs/2509.04255 https://arxiv.org/pdf/2509.04255

On the equivalence invariance of formal category theory
We prove a result of equivalence invariance of formal category theory for statements that can be expressed within an equipment. To do this, we exploit Henry and Bardomiano Martínez's link between Makkai's FOLDS (first order logic with dependent sorts) and abstract homotopy theory. In the process, we construct a model structure on the category DblCat of double categories and double functors, whose trivial fibrations are the double functors that are surjective on objects, full on horizontal and …

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- An algebra modality admitting countably many deriving transformations
Jean-Baptiste Vienney

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Geometric Construction of Quiver Tensor Products
Daigo Ito, John S. Nolan
…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Combs, Causality and Contractions in Atomic Markov Categories
Dario Stein, M\'ark Sz\'eles

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Virtually Gorenstein algebras of infinite dominant dimension
Hongxing Chen, Changchang Xi

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…

[2025-10-08 Wed (UTC), 1 new article found for math.CT Category Theory]
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[2025-09-08 Mon (UTC), 3 new articles found for math.CT Category Theory]
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Zigzags and free adjunctions
Lorenzo Riva, Martina Rovelli
https://arxiv.org/abs/2510.05371 https://arxiv.org/pdf/2510.05371…

Zigzags and free adjunctions
We construct an explicit combinatorial model of the functor which adds right adjoints to the morphisms of an $\infty$-category, and we speculate on possible extensions to higher dimensions.

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- One rig to control them all
Chris Heunen, Robin Kaarsgaard, Louis Lemonnier

Cartesian Linearly Distributive Categories: Revisited
Rose Kudzman-Blais, Jean-Simon Pacaud Lemay
https://arxiv.org/abs/2509.04435 https://arxiv.org/pdf/25…

Cartesian Linearly Distributive Categories: Revisited
Linearly distributive categories (LDC) were introduced by Cockett and Seely to provide an alternative categorical semantics for multiplicative linear logic. In contrast to Barr's $\ast$-autonomous categories, LDCs take multiplicative conjunction and disjunction as primitive notions. Thus, a LDC is a category with two monoidal products that interact via linear distributors. A cartesian linearly distributive category (CLDC) is a LDC whose two monoidal products coincide with categorical products a…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Pseudolimits for Tangent Categories with Applications to Equivariant Algebraic and Differential G...
Dorette Pronk, Geoff Vooys

Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Abstract Cluster Structures
Jan E. Grabowski, Sira Gratz
https://

[2025-10-07 Tue (UTC), 2 new articles found for math.CT Category Theory]
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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.

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…

Internal languages of locally cartesian closed $(\infty,1)$-categories
El Mehdi Cherradi
https://arxiv.org/abs/2509.03371 https://arxiv.org/pdf/2509.03371

Internal languages of locally cartesian closed $(\infty,1)$-categories
We establish a DK-equivalence between the relative category of $π$-tribes and the relative category of locally cartesian closed quasicategories. From this follows one of the internal languages conjecture: Martin-Löf type theory with dependent sums, intensional identity types, and dependent products satisfying functional extensionality is the internal language of locally cartesian closed $(\infty,1)$-categories.