Tootfinder

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…

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…

2-cabling and tangle operators in Khovanov theory
Mihai Marian
https://arxiv.org/abs/2508.00644 https://arxiv.org/pdf/2508.00644

2-cabling and tangle operators in Khovanov theory
We describe an operator on 4-ended tangles that is induced by 2-cabling of a strongly invertible knot. By passing to the 4-ended tangle Khovanov theory of Kotelskiy-Watson-Zibrowius, this induces an operator on the category of type D structures over the Bar-Natan algebra $\mathcal{B}$, as well as on a Fukaya category of the 4-punctured 2-sphere. We provide a full description of this operator's restriction to cap-trivial tangles. Finally, we extract geography results that are inspired by a recen…

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…

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.

Duality for KGL-modules in motivic homotopy theory
Christian Dahlhausen, Jeroen Hekking, Storm Wolters
https://arxiv.org/abs/2508.00064 https://arxiv.org/p…

Duality for KGL-modules in motivic homotopy theory
We prove a duality statement on modules over KH-theory in the stable motivic homotopy category whose dualizing object is given by G-theory, over any quasi-excellent scheme of characteristic zero.

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…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Multicategories from Symmetric Monoidal Categories
A. D. Elmendorf
https://…

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…

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}^…

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…

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…

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…

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…

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

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

[2025-08-04 Mon (UTC), 3 new articles found for math.CT Category Theory]
toXiv_bot_toot

The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory
Lukas Woike
https://arxiv.org/abs/2507.22841 https://arxiv.org/pdf/2507.…

The Construction of Correlators in Finite Rigid Logarithmic Conformal Field Theory
For logarithmic conformal field theories whose monodromy data is given by a not necessarily semisimple modular category, we solve the problem of constructing and classifying the consistent systems of correlators. The correlator construction given in this article generalizes the well-known one for rational conformal field theories given by Fuchs-Runkel-Schweigert roughly twenty years ago and solves conjectures of Fuchs, Gannon, Schaumann and Schweigert. The strategy is, even in the rational spec…

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

Hochschild cohomology and deformation theory of stable infinity-categories with t-structures
Isamu Iwanari
https://arxiv.org/abs/2506.21867 https://…

Hochschild cohomology and deformation theory of stable infinity-categories with t-structures
Given a stable presentable infinity-category $\mathcal{E}$ equipped with a left complete t-structure, we prove that its Hochschild cohomology governs the deformation theory of $\mathcal{E}$ with respect to left complete t-structures.

Stereotype graph: A mathematical framework of category stereotypes via graph theory
Yijia Yan
https://arxiv.org/abs/2506.12533 https://

Stereotype graph: A mathematical framework of category stereotypes via graph theory
In social psychology and cognitive science, there has been much interest in studying category stereotypes. However, we still lack a consensual mathematical definition or framework, which is necessary for us to hold a deeper understanding of stereotypes in human cognition. In this paper, we use graph theory to portray category stereotypes in human cognition, based on pairs of labels having special relations. By using methods and conclusions in graph theory (including algebraic graph theory and v…

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

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…

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

[2025-06-05 Thu (UTC), no new articles found for math.CT Category Theory]
#toXiv_bot_toot

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…

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 …

A modern perspective on rational homotopy theory
Eleftherios Chatzitheodoridis
https://arxiv.org/abs/2505.23322 https://arxiv.org/pdf…

A modern perspective on rational homotopy theory
In Quillen's paper on rational homotopy theory, the category of 1-reduced simplicial sets is endowed with a family of model structures, the most prominent of which is the one whose weak equivalences are the rational homotopy equivalences. In this paper, we give a modern approach to this family of model structures.

This https://arxiv.org/abs/2412.05071 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Motivic Riemann-Roch Theorem for Deligne-Mumford Stacks
We develop a motivic cohomology theory, representable in the Voevodsky's triangulated category of motives, for smooth separated Deligne-Mumford stacks and show that the resulting higher Chow groups are canonically isomorphic to the higher $K$-theory of such stacks. This generalises the Grothendieck-Riemann-Roch theorem to the category of smooth Deligne-Mumford stacks.

Floer homotopy theory for monotone Lagrangians
Ciprian Mircea Bonciocat
https://arxiv.org/abs/2506.17431 https://arxiv.org/pdf/2506.1…

Floer homotopy theory for monotone Lagrangians
We circumvent one of the roadblocks in associating Floer homotopy types to monotone Lagrangians, namely the curvature phenomena occurring in high dimensions. Given $N \ge 3$ and $R$ a connective $\mathbb E_1$-ring spectrum, there is a notion of an $N$-truncated, $R$-oriented flow category, to which we associate a module prospectrum over the Postnikov truncation $τ_{\le N - 3}R$. This endows ordinary Floer cohomology with an action of the Steenrod algebra over $τ_{\le N-3}R$, and also induces …

Cochain valued TQFTs from nonsemisimple modular tensor categories
Agustina Czenky, Cris Negron
https://arxiv.org/abs/2507.17169 https://arxiv.org/pdf/2507.…

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

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…

This https://arxiv.org/abs/2305.04150 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Motivic real topological Hochschild spectrum
We define real topological Hochschild homology of separated log schemes with involutions. We show that real topological Hochschild homology is $(\mathbb{P}^n,\mathbb{P}^{n-1})$-invariant, which leads to the definition of the motivic real topological Hochschild spectrum living in a certain $\mathbb{Z}/2$-equivariant logarithmic motivic category. We explore properties of real topological Hochschild homology that can be deduced from the logarithmic motivic homotopy theory. We also define the motiv…

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…

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)

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

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

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…

[2025-07-03 Thu (UTC), 2 new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-03 Tue (UTC), 4 new articles found for math.CT Category Theory]
#toXiv_bot_toot

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.

Equivariant $KK$-theory and model categories
Anupam Datta, Michael Joachim
https://arxiv.org/abs/2506.16238 https://arxiv.org/pdf/250…

Equivariant $KK$-theory and model categories
We cast Kasparov's equivariant KK-theory in the framework of model categories. We obtain a stable model structure on a certain category of locally multiplicative convex $G$-$C^*$-algebras, which naturally contains the stable $\infty$-category $KK^G_{\operatorname{sep}}$ as described by Bunke, Engel, Land (\cite{BEL}). Non-equivariantly, $KK$-theory was studied using model categories by Joachim-Johnson (\cite{MJ}). We generalize their ideas in the equivariant case, and also fix some critical err…

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

On the ring of cooperations for real Hermitian K-theory
Jackson Morris
https://arxiv.org/abs/2506.16672 https://arxiv.org/pdf/2506.16…

On the ring of cooperations for real Hermitian K-theory
Let kq denote the very effective cover of the motivic Hermitian K-theory spectrum. We analyze the ring of cooperations $π^\mathbb{R}_{**}(\text{kq} \otimes \text{kq})$ in the stable motivic homotopy category $\text{SH}(\mathbb{R})$, giving a full description in terms of Brown--Gitler comodules. To do this, we decompose the $E_2$-page of the motivic Adams spectral sequence and show that it must collapse. The description of the $E_2$-page is accomplished by a series of algebraic Atiyah--Hirzebru…

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

The disoriented skein and iquantum Brauer categories
Hadi Salmasian, Alistair Savage, Yaolong Shen
https://arxiv.org/abs/2507.12328 https://

The disoriented skein and iquantum Brauer categories
We develop a diagrammatic approach to the representation theory of the quantum symmetric pairs corresponding to orthosymplectic Lie superalgebras inside general linear Lie superalgebras. Our approach is based on the disoriented skein category, which we define as a module category over the framed HOMFLYPT skein category. The disoriented skein category admits full incarnation functors to the categories of modules over the iquantum enveloping algebras corresponding to the quantum symmetric pairs, …

The spectrum of global representations for families of bounded rank and VI-modules
Miguel Barrero, Tobias Barthel, Luca Pol, Neil Strickland, Jordan Williamson
https://arxiv.org/abs/2506.21525

The spectrum of global representations for families of bounded rank and VI-modules
A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups belonging to a family $\mathscr{U}$. These arise in classical representation theory, in the study of representation stability, as well as in global homotopy theory. In this paper we begin a systematic study of the derived category $\mathsf{D}(\mathscr{U};k)$ of global representations over fields $k$ of characteristic zero, from the point-of-view of tensor-triangular geomet…

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.

Segal K-theory factors through Waldhausen categories
Maxine E. Calle, David Chan
https://arxiv.org/abs/2506.13732 https://arxiv.org/p…

Segal K-theory factors through Waldhausen categories
We show that Segal's K-theory of symmetric monoidal categorizes can be factored through Waldhausen categories. In particular, given a symmetric monoidal category $C$, we produce a Waldhausen category $Γ(C)$ whose K-theory is weakly equivalent to the Segal K-theory of $C$. As a consequence, we show that every connective spectrum may be obtained via Waldhausen K-theory.

Covering techniques in higher Auslander-Reiten theory
Javad Asadollahi, Rasool Hafezi, Zohreh Sourani, Razieh Vahed
https://arxiv.org/abs/2506.16268 https:…

Covering techniques in higher Auslander-Reiten theory
This paper investigates the behavior of $n$-precluster tilting subcategories under the push-down functor in the context of Galois coverings of locally bounded categories. Building on higher Auslander-Reiten theory and covering techniques, we establish that for a locally support-finite category $\mathcal{C}$ with a free group action $G$ on its indecomposables, the push-down functor maps $G$-equivariant $n$-precluster tilting subcategories of ${\rm mod}\mbox{-}\mathcal{C}$ to $n$-precluster tilti…

[2025-07-02 Wed (UTC), 2 new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-02 Mon (UTC), no new articles found for math.CT Category Theory]
#toXiv_bot_toot

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- A weight-formula for all highest weight modules, and a higher order parabolic category $\mathcal{O}$
Apoorva Khare, G. Krishna Teja

An isovariant Blakers--Massey theorem
Inbar Klang, Sarah Yeakel
https://arxiv.org/abs/2506.21259 https://arxiv.org/pdf/2506.21259

An isovariant Blakers--Massey theorem
An isovariant map is an equivariant map between $G$-spaces which strictly preserves isotropy groups. In this paper, we lay the groundwork for the study of isovariant stable homotopy theory. We prove an isovariant Blakers--Massey theorem and its $n$-cubical generalization, define a suitable notion of suspension (by a trivial representation sphere) in the isovariant category, and prove an isovariant Freudenthal suspension theorem.

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…

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

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

[2025-08-01 Fri (UTC), 2 new articles found for math.CT Category Theory]
toXiv_bot_toot

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

This https://arxiv.org/abs/2505.18329 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Towards a double operadic theory of systems
We present a unified framework for categorical systems theory which packages a collection of open systems, their interactions, and their maps into a symmetric monoidal loose right module of systems over a symmetric monoidal double category of interfaces and interactions. As examples, we give detailed descriptions of (1) the module of open Petri nets over undirected wiring diagrams and (2) the module of deterministic Moore machines over lenses. We define several pseudo-functorial constructions o…

A Model of Type Theory in Groupoid Assemblies
Anthony Agwu
https://arxiv.org/abs/2507.16062 https://arxiv.org/pdf/2507.16062

A Model of Type Theory in Groupoid Assemblies
We consider the category $\GrpA{A}$ of groupoids defined internally to the category of assemblies on a partial combinatory algebra $A$. In this thesis we exhibit the structure of a $π$-tribe on $\GrpA{A}$ showing the category to be a model of type theory. We also show that $\GrpA{A}$ has $W$-types with reductions and univalent object classifier for assemblies and modest assemblies, where the latter is an impredicative object classifier. Using the $W$-types with reductions, we show that $\GrpA{…

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

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

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

[2025-07-31 Thu (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-30 Mon (UTC), 2 new articles found for math.CT Category Theory]
toXiv_bot_toot

Sheaves on a bicategory
Olivia Caramello, Elio Pivet
https://arxiv.org/abs/2507.20820 https://arxiv.org/pdf/2507.20820

Sheaves on a bicategory
We give a detailed account of the theory of enrichment over a bicategory and show that it establishes a two-fold generalization of enrichment over both quantaloids and monoidal categories. We define complete B-categories, a generalization of Cauchy-complete enriched categories serving as a basis for the development of sheaf theory in the enriched setting. We prove an adjunction between complete B-categories and 2-presheaves on the category Map(B) of left adjoints in B. We express conditions und…

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

[2025-07-30 Wed (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-05-30 Fri (UTC), 2 new articles found for math.CT Category Theory]
#toXiv_bot_toot

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

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

The homological spectrum for monoidal triangulated categories
Daniel K. Nakano, Kent B. Vashaw, Milen T. Yakimov
https://arxiv.org/abs/2506.19946 https://

The homological spectrum for monoidal triangulated categories
The authors develop a notion of homological prime spectrum for an arbitrary monoidal triangulated category, ${\mathbf C}$. Unlike the symmetric case due to Balmer, the homological primes of ${\mathbf C}$ are not defined as the maximal Serre ideals of the small module category ${\sf mod}\text{-}{\mathbf C}$, or via a noncommutative ring theory inspired version of this construction. Instead, the authors work with an extended comparison map from the Serre prime spectrum $\operatorname{Spc} ({\sf m…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- On pure monomorphisms and pure epimorphisms in accessible categories
Leonid Positselski

[2025-07-29 Tue (UTC), 3 new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-05-29 Thu (UTC), no new articles found for math.CT Category Theory]
#toXiv_bot_toot

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Monoidal Envelopes of Families of $\infty$-Operads and $\infty$-Operadic Kan Extensions
Kensuke Arakawa

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Unstable independence from the categorical point of view
Mark Kamsma, Ji\v{r}\'i Rosick\'y

[2025-07-28 Mon (UTC), 1 new article found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-27 Fri (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-05-28 Wed (UTC), 1 new article found for math.CT Category Theory]
#toXiv_bot_toot

This https://arxiv.org/abs/2409.10438 has been replaced.
link: https://scholar.google.com/scholar?q=a

A functorial approach to $n$-abelian categories
We develop a functorial approach to the study of $n$-abelian categories by reformulating their axioms in terms of their categories of finitely presented functors. Such an approach allows the use of classical homological algebra and representation theory techniques to understand higher homological algebra. As an application, we present two possible generalizations of the axioms "every monomorphism is a kernel" and "every epimorphism is a cokernel" of an abelian category to $n$-abelian categories…

This https://arxiv.org/abs/2503.17274 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Composable Uncertainty in Symmetric Monoidal Categories for Design Problems
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging wires, or compact closed structures for feedback. A key example is the compact closed SMC of design problems (DP), which enables a compositional approach to co-design in engineering. However, in practice, the systems of interest may not be fully known. Recent…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Additive Invariants of Open Petri Nets
Benjamin Merlin Bumpus, Sophie Libkind, Jordy Lopez Garcia, Layla Sorkatti, Samuel Tenka

[2025-06-26 Thu (UTC), 2 new articles found for math.CT Category Theory]
toXiv_bot_toot

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Rewriting techniques for relative coherence
Samuel Mimram
https://

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Representations over diagrams of abelian categories II: Abelian model structures
Zhenxing Di, Liping Li, Li Liang, Nina Yu

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Note on the linearisation of finite abelian groups
Aur\'elien Djament (CNRS, LAGA)

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Rewriting techniques for relative coherence
Samuel Mimram

[2025-06-25 Wed (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-07-25 Fri (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-24 Tue (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- An Algebraic Extension of Intuitionistic Linear Logic: The $L_!^S$-Calculus and Its Categorical M...
Alejandro D\'iaz-Caro, Malena Ivnisky, Octavio Malherbe

[2025-07-24 Thu (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-23 Mon (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Rewriting techniques for relative coherence
Samuel Mimram

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
Are chain-complete posets co-wellpowered?
https://

[2025-07-23 Wed (UTC), 1 new article found for math.CT Category Theory]
toXiv_bot_toot

[2025-07-22 Tue (UTC), 3 new articles found for math.CT Category Theory]
toXiv_bot_toot

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Action accessible and weakly action representable varieties of algebras
Xabier Garc\'ia-Mart\'inez, Manuel Mancini

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
Double groupoids and $2$-groupoids in regular Mal'tsev categories

[2025-07-21 Mon (UTC), 1 new article found for math.CT Category Theory]
toXiv_bot_toot

[2025-06-20 Fri (UTC), no new articles found for math.CT Category Theory]
toXiv_bot_toot