Tootfinder

The presentable stable envelope of an exact category
Christoph Winges, Marius Nielsen
https://arxiv.org/abs/2506.02598 https://arxiv.…

The presentable stable envelope of an exact category
We prove an analogue of the Gabriel--Quillen embedding theorem for exact $\infty$-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact $\infty$-category. Moreover, we construct a symmetric monoidal structure on the $\infty$-category of small exact $\infty$-categories and discuss the multiplicative properties of the Gabriel--Quillen embedding. For $E$ an Adams-type homotopy associative ring spectrum, this allows us to identify the symmetric monoidal $\infty$-…

The 1-periodic derived category of a gentle algebra : Part 1 -- Indecomposable objects
Joseph Winspeare
https://arxiv.org/abs/2506.04012 https://

The 1-periodic derived category of a gentle algebra : Part 1 -- Indecomposable objects
Combining results from Keller and Buchweitz, we describe the 1-periodic derived category of a finite dimensional algebra $A$ of finite global dimension as the stable category of maximal Cohen-Macaulay modules over some Gorenstein algebra $A^\ltimes$. In the case of gentle algebras, using the geometric model introduced by Opper, Plamondon and Schroll, we describe indecomposable objects in this category using homotopy classes of curves on a surface. In particular, we associate a family of indecom…

High-Order Deep Meta-Learning with Category-Theoretic Interpretation
David H. Mguni
https://arxiv.org/abs/2507.02634 https://arxiv.or…

High-Order Deep Meta-Learning with Category-Theoretic Interpretation
We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative mechanism that creates \emph{virtual tasks} -- synthetic problem instances designed to enable the meta-learner to learn \emph{soft constraints} and unknown generalisable rules across related tasks. Crucially, this enables the framework to generate its own infor…

"The places that need to worry are those that look vulnerable or unlikely to fight back. Greenland may fall into that category — which suggests that Denmark and the EU need to find ways of letting Trump know that there will be a price to pay if he makes a move on the island"
Trump always chickens out on foreign policy too - https://on.ft.com/458Z5FI v

This https://arxiv.org/abs/2111.14796 has been replaced.
link: https://scholar.google.com/scholar?q=a

Familial Monads as Higher Category Theories
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any higher category structure which arises as algebras for a familially representable monad on a presheaf category, then use this to describe several examples relating to higher category theory and cubical sets. The proof of this characterization avoids tedious natur…

The TSA is in the same category as ICE in terms of what fucking cruel shit it pulls.
https://unionrayo.com/en/tsa-ban-children-toys-flight/

Goodbye to children's toys on flights - the TSA bans these common items in carry-on luggage
The Transportation Security Administration (TSA) has started confiscating one of the most common items in the carry-on luggage of young children: stuffed

The @… crew are doing a group order of meshtastic wireless devices.
We've selected the Wismesh Pocket v2 plus a small card sized sensor / buzzer. These connect up to 7 hops and we'll be installing 2 solar powered repeaters in Gastown & Mt Pleasant (as well as direct between any two devices)
Fill out the form …

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…

This https://arxiv.org/abs/2505.07960 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$C^\ast$-categorical prefactorization algebras for superselection sectors and topological order
This paper presents a conceptual and efficient geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the $n$-dimensional lattice $\mathbb{Z}^n$. It is shown that, under certain assumptions which are implied by Haag duality, the monoidal $C^\ast$-categories of localized superselection sectors carry the structure of a locally constant prefactorization algebra over the category of cone-shaped subsets of $\mathbb{Z}^…

Welp, looks like I'll need to file a bill to require that if the state is going to assert copyright over its historical markers, it's gotta be under a copyleft license: https://commons.wikimedia.org/wiki/Commons:Deletion_requests/Files_in_Category:Historical_markers_in_New_Hampshire
(that is, assuming something can't be worked out independently without one...)

An algorithm to determine LS-category and Ginsburg invariant of any rationally elliptic space
M. T. K. Abassi, A. Acharqy, K. Boutahir, Y. Rami
https://arxiv.org/abs/2507.02590

An algorithm to determine LS-category and Ginsburg invariant of any rationally elliptic space
Let $X$ be a rationally elliptic space. Utilizing the Gorenstein algebra structure of $X$, we present three algorithms that together induce a generating class of $Ext^N_{(ΛV,d)}(\mathbb{Q},(ΛV,d))$ with $N$ being the formal dimension of $X$. From these algorithms, we derive an algorithm to compute the rational Lusternik-Schnirelmann category $cat_0(X)$. Furthermore, by applying a spectral sequence argument based on the {\it Eilenberg-Moore spectral sequence}, we compute the rational Ginsburg …

This https://arxiv.org/abs/2207.12969 has been replaced.
link: https://scholar.google.com/scholar?q=a

Module Categories of the Generic Virasoro VOA and Quantum Groups
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group $\mathcal{U}_q (\mathfrak{sl}_{2})$ with $q$ determined by the central charge. This is a continuation of…

Group schemes and their Lie algebras over a symmetric tensor category
Dave Benson, Julia Pevtsova
https://arxiv.org/abs/2507.02031 https://

Group schemes and their Lie algebras over a symmetric tensor category
We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as the degree one distributions on the group scheme, or as the right invariant derivations on the coordinate ring. In the second half of the paper, we illustrate the theory in the particular case of the symmetric tensor category $\mathsf{Ver}_4^+$ in characteristi…

Selecting Apparel as my 5 percent cash-back category on a certain debit card this month was probably ill-advised

The Gauss-Markov Adjunction: Categorical Semantics of Residuals in Supervised Learning
Moto Kamiura
https://arxiv.org/abs/2507.02442 https://

The Gauss-Markov Adjunction: Categorical Semantics of Residuals in Supervised Learning
Enhancing the intelligibility and interpretability of machine learning is a crucial task in responding to the demand for Explicability as an AI principle, and in promoting the better social implementation of AI. The aim of our research is to contribute to this improvement by reformulating machine learning models through the lens of category theory, thereby developing a semantic framework for structuring and understanding AI systems. Our categorical modeling in this paper clarifies and formalize…

This https://arxiv.org/abs/2505.22171 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

2-Category of Topological Quantum Computation
Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of Hilb. In this paper, we argue that a categorical formalism that captures and unifies both anyonic theories (the Hardware of quantum computing) and a model of top…

Multiplicity in triangulated categories
Petter Andreas Bergh, David A. Jorgensen, Peder Thompson
https://arxiv.org/abs/2506.02437 https://

Multiplicity in triangulated categories
We lay out the theory of a multiplicity in the setting of a triangulated category having a central ring action from a graded-commutative ring $R$, in other words, an $R$-linear triangulated category. The invariant we consider is modelled on those for graded modules over a commutative graded ring. We show that this invariant is determined by the leading coefficients of the Hilbert polynomials expressing the lengths of certain Hom sets. Our theory is a natural analogue of Hochster's theta invaria…

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

Universal property of framed $G$-disc algebras
Aleksandar Miladinovi\'c
https://arxiv.org/abs/2506.02699 https://arxiv.org/pdf/25…

Universal property of framed $G$-disc algebras
Given a compact Lie group $G$ and its finite subgroup $H$ we prove that the $\infty$-category of $G/H$-framed $G$-disc algebras taking values in a $G$-symmetric monoidal category $\underline{\mathcal{C}}^{\otimes}$ is equivalent to the $\infty$-category of $V$-framed $H$-disc algebras (where $V$ is an $H$-representation) which take values in $\underline{\mathcal{C}}^{\otimes}_H$, the underlying $H$-symmetric monoidal subcategory of $\underline{\mathcal{C}}^{\otimes}$. We will use this construct…

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…

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…

This https://arxiv.org/abs/2403.04088 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The classification of endotrivial complexes
Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We give a complete classification of endotrivial complexes, i.e. determine the Picard group $\mathcal{E}_k(G)$ of the tensor-triangulated category $K^b({}_{kG}\mathbf{triv})$, the bounded homotopy category of $p$-permutation modules, which Balmer and Gallauer recently considered. For $p$-groups, we identify $\mathcal{E}_k(-)$ with the rational $p$-biset functor $CF_b(-)$ of Borel-Smith functions and recover a short exact seq…

A Statistics-Driven Differentiable Approach for Sound Texture Synthesis and Analysis
Esteban Guti\'errez, Frederic Font, Xavier Serra, Lonce Wyse
https://arxiv.org/abs/2506.04073

A Statistics-Driven Differentiable Approach for Sound Texture Synthesis and Analysis
In this work, we introduce TexStat, a novel loss function specifically designed for the analysis and synthesis of texture sounds characterized by stochastic structure and perceptual stationarity. Drawing inspiration from the statistical and perceptual framework of McDermott and Simoncelli, TexStat identifies similarities between signals belonging to the same texture category without relying on temporal structure. We also propose using TexStat as a validation metric alongside Frechet Audio Dista…

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

Flowing Loops
Great Australian Pods Podcast Directory: #GreatAusPods

Flowing Loops | Great Australian Pods Podcast Directory
Podcast: Flowing Loops Host: Dan Koop Category: Arts Sub-Category: Crafts & Creativity, Local News & Stories, Places & Travel First Episode: 2024 Dan Koop and six artists have been walking and talking…

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…

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.

Wild Betti sheaves
Peter Scholze
https://arxiv.org/abs/2505.24599 https://arxiv.org/pdf/2505.24599

Wild Betti sheaves
In this note, we consider the problem of constructing an enlargement of the category of Betti sheaves that supports an ``exponential local system'' on $\mathbb R$, and a Fourier equivalence defined on all sheaves. We show that there is a universal solution, recovering a construction of Tamarkin known also as ``enhanced sheaves''. The universality property implies that the category of coefficients of this theory is, in a suitable sense, a nontrivial $\mathbb R_{>0}$-torsor over $\mathrm{Spec}(\m…

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.

SplArt: Articulation Estimation and Part-Level Reconstruction with 3D Gaussian Splatting
Shengjie Lin, Jiading Fang, Muhammad Zubair Irshad, Vitor Campagnolo Guizilini, Rares Andrei Ambrus, Greg Shakhnarovich, Matthew R. Walter
https://arxiv.org/abs/2506.03594

SplArt: Articulation Estimation and Part-Level Reconstruction with 3D Gaussian Splatting
Reconstructing articulated objects prevalent in daily environments is crucial for applications in augmented/virtual reality and robotics. However, existing methods face scalability limitations (requiring 3D supervision or costly annotations), robustness issues (being susceptible to local optima), and rendering shortcomings (lacking speed or photorealism). We introduce SplArt, a self-supervised, category-agnostic framework that leverages 3D Gaussian Splatting (3DGS) to reconstruct articulated ob…

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.

This https://arxiv.org/abs/2412.05927 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Abstract categorical residues and Calabi-Yau structures
Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincaré-Lefschetz duality of dimension n has a boundary which itself satisfies Poincaré duality of dimension n, we show that the categorical formal punctured neighborhood of infinity, a canonical categorical construction associated to every $A_{\infty}$ category, has a weak proper Calabi-Yau structure of dimension n-1 whenever the original $A_{\infty}$ category admits a weak smooth Calabi-Yau stru…

Classification of exact structures using the Ziegler spectrum
Julia Sauter
https://arxiv.org/abs/2506.02304 https://arxiv.org/pdf/250…

Classification of exact structures using the Ziegler spectrum
Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak cokernels, this topological space is an open subset of the Ziegler spectrum and this is a result of Kevin Schlegel. We also look at some module categories of rings where the Ziegler spectrum is known and calculate the global dimensi…

This https://arxiv.org/abs/2406.18497 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The equivariant model structure on cartesian cubical sets
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved Eilenberg-Zilber category. The key innovation is an additional equivariance condition in the specification of the cubical Kan fibrations, which can be described as the pullback of an interval-based class of uniform fibrations in the category of symmetric sequences of cu…

[2025-07-04 Fri (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

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-exploitat…

Finance Friends
Great Australian Pods Podcast Directory: #GreatAusPods

Finance Friends | Great Australian Pods Podcast Directory
Podcast: Finance Friends Host: Fabian Ruggieri Category: Business Sub-Category: Finance & Investing First Episode: 2024 Imagine getting insider knowledge from industry leaders every week.

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…

This https://arxiv.org/abs/2305.08943 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Cosmology of Single Species Hidden Dark Matter
Cosmology and astrophysics provide various ways to study the properties of dark matter even if they have negligible non-gravitational interactions with the Standard Model particles and remain hidden. We study a type of hidden dark matter model in which the dark matter is completely decoupled from the Standard Model sector except gravitationally, and consists of a single species with conserved comoving particle number and conserved comoving entropy. This category of hidden dark matter includes m…

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…

This https://arxiv.org/abs/2504.07884 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

CatCMA with Margin: Stochastic Optimization for Continuous, Integer, and Categorical Variables
This study focuses on mixed-variable black-box optimization (MV-BBO), addressing continuous, integer, and categorical variables. Many real-world MV-BBO problems involve dependencies among these different types of variables, requiring efficient methods to optimize them simultaneously. Recently, stochastic optimization methods leveraging the mechanism of the covariance matrix adaptation evolution strategy have shown promising results in mixed-integer or mixed-category optimization. However, such …

[2025-06-04 Wed (UTC), 3 new articles found for math.CT Category Theory]
#toXiv_bot_toot

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.

[2025-06-05 Thu (UTC), no new articles found for math.CT Category Theory]
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Confessions Radio
Great Australian Pods Podcast Directory: #GreatAusPods

Confessions Radio | Great Australian Pods Podcast Directory
Podcast: Confessions Radio Hosts: Amma and Chrystal Category: Comedy Sub-Category: Comedy Interviews & Chats, Personal Stories First Episode: 2022 Confessions is the go-to discussion space for all…

This https://arxiv.org/abs/2501.06486 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Combinatorial quantization of 4d 2-Chern-Simons theory I: the Hopf category of higher-graph states
2-Chern-Simons theory, or more commonly known as 4d BF-BB theory with gauged shift symmetry, is a natural generalization of Chern-Simons theory to 4-dimensional manifolds. It is part of the bestiary of higher-homotopy Maurer-Cartan theories. In this article, we present a framework towards the combinatorial quantization of 2-Chern-Simons theory on the lattice, taking inspiration from the work of Aleskeev-Grosse-Schomerus three decades ago. The central geometric input is the 2-truncation $Γ^2$ o…

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…

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.

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.

The Pursuit Of MiSELF
Great Australian Pods Podcast Directory: #GreatAusPods

The Pursuit Of MiSELF | Great Australian Pods Podcast Directory
Podcast: The Pursuit Of MiSELF Host: Rayne Bryant Category: Education Sub-Category: Self Development & Advice First Episode: 2025 Here we take ownership of our healing, we rewrite the rules…

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.

An isometry theorem for persistent homology of circle-valued functions
Nathan Broomhead, Mariam Pirashvili
https://arxiv.org/abs/2506.02999 https://…

An isometry theorem for persistent homology of circle-valued functions
This paper explores persistence modules for circle-valued functions, presenting a new extension of the interleaving and bottleneck distances in this setting. We propose a natural generalisation of barcodes in terms of arcs on a geometric model associated to the derived category of quiver representations. The main result is an isometry theorem that establishes an equivalence between the interleaving distance and the bottleneck distance for circle-valued persistence modules.

This https://arxiv.org/abs/2501.17769 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Colimits of internal categories
We show that for an extensive $1$-category $\mathcal{E}$ with pullbacks and pullback stable coequalisers in which the forgetful functor $\mathcal{U}: \mathbf{Cat}(\mathcal{E})_1 \to \mathbf{Gph}(\mathcal{E})$ has left adjoint, the $2$-category $\mathbf{Cat}(\mathcal{E})$ of internal categories, functors and natural transformations has finite $2$-colimits. In addition, $\mathbf{Cat}(\mathcal{E})$ is extensive, has pullbacks and codescent coequalisers are stable under pullback along discrete Cond…

This https://arxiv.org/abs/2402.11852 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Forcing techniques for Cichoń's Maximum: Lecture notes for the mini-course at the University of Vienna
Cichoń's diagram describes the connections between combinatorial notions related to measure, category, and compactness of sets of irrational numbers. In the second part of the 2010's, Goldstern, Kellner and Shelah constructed a forcing model of Cichoń's Maximum (meaning that all non-dependent cardinal characteristics are pairwise different) by using large cardinals. Some years later, we eliminated this large cardinal assumption. In this mini-course, we explore the forcing techniques to constr…

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…

This https://arxiv.org/abs/1712.00555 has been replaced.
link: https://scholar.google.com/scholar?q=a

A monadicity theorem for higher algebraic structures
We develop a theory of Eilenberg-Moore objects in any $(\infty,2)$-category and extend Barr-Beck's monadicity theorem to any $(\infty,2)$-category that admits Eilenberg-Moore objects. We apply this result to various $(\infty,2)$-categories of higher algebraic structures to obtain a monadicity theorem for enriched $\infty$-categories, $\infty$-operads and higher Segal objects. Analyzing Eilenberg-Moore objects in the $(\infty,2)$-categories of symmetric monoidal $\infty$-categories and lax (opla…

Benchmarking Adelaide
Great Australian Pods Podcast Directory: #GreatAusPods

Benchmarking Adelaide | Great Australian Pods Podcast Directory
Podcast: Benchmarking Adelaide Host: Sam Dighton Category: Society & Culture Sub-Category: Entrepreneurship, Local News & Stories, Mathematics & Data Science First Episode: 2024 We sit down with…

A remark on Continuous K-theory and Fourier-Sato transform
Bingyu Zhang
https://arxiv.org/abs/2506.02329 https://arxiv.org/pdf/2506.0…

A remark on Continuous K-theory and Fourier-Sato transform
In this note, we prove a generalization of Efimov's computation for the universal localizing invariant of categories of sheaves with certain microsupport constraints. The proof is based on certain categorical equivalences given by the Fourier-Sato transform, which is different from the original proof. As an application, we compute the universal localizing invariant of the category of almost quasi-coherent sheaves on the Novikov toric scheme introduced by Vaintrob.

This https://arxiv.org/abs/2408.05103 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Koszul duality for generalised Steinberg representations of $p$-adic groups
Let $G$ be a semisimple group, split over a non-Archimedean field $F$. We prove that the category of modules over the extension algebra of generalised Steinberg representations of $G(F)$ is equivalent to a full subcategory of equivariant perverse sheaves on the variety of Langlands parameters for these representations. Specifically, we establish an equivalence \[ \textbf{Mod}(\text{Ext}_G^\bullet(Σ_λ, Σ_λ)) \simeq \textbf{Per}_{\widehat{G}}^\circ(X_λ), \] where $Σ_λ$ is the direct sum of…

This https://arxiv.org/abs/2503.17319 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The algebraic internal groupoid model of Martin-Löf type theory
We extend the model structure on the category $\mathbf{Cat}(\mathcal{E})$ of internal categories studied by Everaert, Kieboom and Van der Linden to an algebraic model structure. Moreover, we show that it restricts to the category of internal groupoids. We show that in this case, the algebraic weak factorisation system that consists of the algebraic trivial cofibrations and algebraic fibrations forms a model of Martin-Löf type theory. Taking $\mathcal{E} = \mathbf{Set}$ and forgetting the algeb…

Something To Talk About
Great Australian Pods Podcast Directory: #GreatAusPods

Something To Talk About | Great Australian Pods Podcast Directory
Podcast: Something To Talk About Host: Sarrah Le Marquand Category: Society & Culture Sub-Category: Commentary & Conversations, Entertainment News First Episode: 2021 When Australia’s celebrities are…

This https://arxiv.org/abs/2001.09029 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rewriting Structured Cospans
To support the study of compositional networks, we further develop the formalism of structured cospans. To enable rewriting, we introduce a category whose objects are structured cospans and characterize conditions under which this category is a topos or is adhesive. We then define a structured cospan grammar and language, using a 2-category framework. As an application, we demonstrate that for various sorts of graphs, hypergraphs, and Petri nets, any grammar induces the same language as its cor…

Linearly Distributive Fox Theorem
Rose Kudzman-Blais
https://arxiv.org/abs/2506.02180 https://arxiv.org/pdf/2506.02180

Linearly Distributive Fox Theorem
Linearly distributive categories (LDC), introduced by Cockett and Seely to model multiplicative linear logic, are categories equipped with two monoidal structures that interact via linear distributivities. A seminal result in monoidal category theory is the Fox theorem, which characterizes cartesian categories as symmetric monoidal categories whose objects are equipped with canonical comonoid structures. The aim of this work is to extend the Fox theorem to LDCs and characterize the subclass of …

This https://arxiv.org/abs/2408.04094 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On endosplit $p$-permutation resolutions and Broué's conjecture for $p$-solvable groups
Endosplit $p$-permutation resolutions play an instrumental role in verifying Broué's abelian defect group conjecture in numerous cases. In this article, we give a complete classification of endosplit $p$-permutation resolutions and reduce the question of Galois descent of an endosplit $p$-permutation resolution to the Galois descent of the module it resolves. This is shown using techniques from the study of endotrivial complexes, the invertible objects of the bounded homotopy category of $p$-p…

The algebraic small object argument as a saturation
Evan Cavallo, Christian Sattler
https://arxiv.org/abs/2506.02759 https://arxiv.or…

The algebraic small object argument as a saturation
We analyze the structure of left maps in algebraic weak factorization systems constructed using Garner's algebraic small object argument. We find that any left map can be constructed from generators in Bourke and Garner's double category of left maps by operations that parallel the classical cell-complex-forming operations of Quillen's small object argument (coproducts, cobase changes, transfinite composites, and retracts). Our main theorems are phrased as "saturation" principles, which express…

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…

Artist's Gotta Eat
Great Australian Pods Podcast Directory: #GreatAusPods

Artist’s Gotta Eat | Great Australian Pods Podcast Directory
Podcast: Artist’s Gotta Eat Host: Brad Shean Category: Arts Sub-Category: Careers, Performing Arts & Music, Stand Up Comedy First Episode: 2025 We dig into the business side of Show Business as we…

This https://arxiv.org/abs/2503.10524 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the computation of the vanishing locus of a finitely presented functor
We discuss invariants which are helpful for the computation of the vanishing locus of a finitely presented functor $\mathcal{G}$, i.e., the set of points in the Ziegler spectrum on which $\mathcal{G}$ vanishes. These invariants are: the rank of $\mathcal{G}$, the supports of its co- and contravariant defect, and the class of $\mathcal{G}$ in the Grothendieck group of the category of finitely presented functors. We show that these invariants determine the vanishing locus in the case of a finitel…

Bochner-type theorems for distributional category
Ekansh Jauhari, John Oprea
https://arxiv.org/abs/2505.21763 https://arxiv.org/pdf/2…

Bochner-type theorems for distributional category
We show that in the presence of a geometric condition such as non-negative Ricci curvature, the distributional category of a manifold may be used to bound invariants, such as the first Betti number and macroscopic dimension, from above. Moreover, à la Bochner, when the bound is an equality, special constraints are imposed on the manifold. We show that the distributional category of a space also bounds the rank of the Gottlieb group, with equality imposing constraints on the fundamental group. …

Teach Us Consent
Great Australian Pods Podcast Directory: #GreatAusPods

Teach Us Consent | Great Australian Pods Podcast Directory
Podcast: Teach Us Consent Host: Anthony Stefanos Category: Society & Culture Sub-Category: Relationships & Sexuality First Episode: 2025 Get confident with consent, sex and relationships – one honest…

Dont Make Me Call Her
Great Australian Pods Podcast Directory: #GreatAusPods

Don’t Make Me Call Her | Great Australian Pods Podcast Directory
Podcast: Dont Make Me Call Her Host: Grace Lam Category: Comedy Sub-Category: Comedy Chats & Interviews First Episode: 2024 What can a former Vogue fashion editor talk about? Fashion? Nah—way more!

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.

Support 4 Employment Podcast
Great Australian Pods Podcast Directory: #GreatAusPods

Support 4 Employment | Great Australian Pods Podcast Directory
Podcast: Support 4 Employment Podcast Host: Scott Category: Business Sub-Category: Careers, Commentary & Conversations, Health & Wellness, Non Profit & Charity First Episode: 2025 Join a rotating crew…

Saturday Breakfast With Julie Reynolds - The "Best Bits"
Great Australian Pods Podcast Directory: https://www.greataustralianpods.com/saturday-breakfast-with-julie-reynolds-the-best-bits/

Saturday Breakfast | Great Australian Pods Podcast Directory
Podcast: Saturday Breakfast With Julie Reynolds – The “Best Bits” Host: Julie Reynolds Category: Arts Sub-Category: Commentary & Conversations, Entertainment News First Episode: 2022 A podcast made…

This https://arxiv.org/abs/2403.15001 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Torsion pairs in categories of modules on ringed finite sites
Let $\mathcal{C}$ be a small category. In this paper, we mainly study the category of modules $\mathfrak{M}\mbox{od-}\mathfrak{R}$ on ringed sites $(\mathbf{C},\mathfrak{R})$. We firstly reprove the Theorem A of the paper (M. Wu and F. Xu. Skew category algebras and modules on ringed finite sites. J. A. 631, 2023), then we characterize $\mathfrak{M}\mbox{od-}\mathfrak{R}$ in terms of the torsion modules on $Gr(\mathfrak{R})$, where $Gr(\mathfrak{R})$ is the linear Grothendieck construction of $…

So You Want To Be A Copywriter With Bernadette Schwerdt
Great Australian Pods Podcast Directory: https://www.greataustralianpods.com/so-you-want-to-be-a-copywriter-with-bernadette-schwerdt/

So You Want To Be A Copywriter | Great Australian Pods Podcast Directory
Podcast: So You Want To Be A Copywriter With Bernadette Schwerdt Host: Bernadette Schwerdt Category: Business Sub-Category: Careers, How To, Marketing & Social Media First Episode: 2021 Join Australia’…

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…

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…

[2025-07-03 Thu (UTC), 2 new articles found for math.CT Category Theory]
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[2025-06-03 Tue (UTC), 4 new articles found for math.CT Category Theory]
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Words On Wednesday
Great Australian Pods Podcast Directory: #GreatAusPods

Words On Wednesday | Great Australian Pods Podcast Directory
Podcast: Words On Wednesday Host: Sylvia Rosenblum Category: Arts Sub-Category: Commentary & Conversations First Episode: 2019 Sylvia Rosenblum, Presenter of Arts Wednesday…

This https://arxiv.org/abs/2401.06584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and linear contractions in terms of simple category-theoretic structures and properties that do not refer to norms, continuity, or real numbers. This builds on Heunen, Kornell, and Van der Schaaf's easier characterisation of the category of all Hilbert spaces and lin…

Dis Dat With My Cousin Vlad
Great Australian Pods Podcast Directory: #GreatAusPods

Dis Dat With My Cousin Vlad | Great Australian Pods Podcast Directory
Podcast: Dis Dat With My Cousin Vlad Host: My Cousin Vlad Category: Comedy Sub-Category: Comedy Interviews & Chats, Stand Up Comedy First Episode: 2020 My Cousin Vlad sits down weekly to go down…

Bravo Bravo Effing Bravo
Great Australian Pods Podcast Directory: #GreatAusPods

Bravo Bravo Effing Bravo | Great Australian Pods Podcast Directory
Podcast: Bravo Bravo Effing Bravo Hosts: Nathan and Mariana Category: TV & Movies Sub-Category: After Shows & Reality TV First Episode: 2021 Bravo Bravo Effing Bravo is a place where you can hear no…

This https://arxiv.org/abs/2407.01203 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An elementary proof of a criterion for subfunctors of Ext to be closed
Let $\mathcal{A}$ be an abelian category and let $F$ be a subbifunctor of the additive bifunctor $\text{Ext}_{\mathcal{A}}^{1}(-,-)\colon \mathcal{A}^{\text{op}}\times \mathcal{A}\to \mathsf{Ab}$. Buan proved in [4] that $F$ is closed if, and only if, $F$ has the $3\times 3$-lemma property, a certain diagrammatic property satisfied by the class of $F$-exact sequences. The proof of this result relies on the theory of exact categories and on the Freyd--Mitchell embedding theorem, a very well-know…

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.

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.

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…

This https://arxiv.org/abs/2406.13240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$ω$-weak equivalences between weak $ω$-categories
We study $ω$-weak equivalences between weak $ω$-categories in the sense of Batanin-Leinster. Our $ω$-weak equivalences are strict $ω$-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict $ω$-categories, they coincide with the weak equivalences in the model category of strict $ω$-categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of $ω$-weak equivalences has the 2-out-of-3 property. We also consider a gene…

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)

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…

[2025-07-02 Wed (UTC), 2 new articles found for math.CT Category Theory]
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[2025-06-02 Mon (UTC), no new articles found for math.CT Category Theory]
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This https://arxiv.org/abs/2501.08559 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$\mathsf{Q}\text{-}\mathbf{Set}$ is not generally a topos
For a commutative, unital and divisible quantale $\mathsf{Q}$, it is shown that the category of $\mathsf{Q}$-sets is a topos if, and only if, $\mathsf{Q}$ is a frame.

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…

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

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,…

[2025-07-01 Tue (UTC), 7 new articles found for math.CT Category Theory]
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