Tootfinder

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…

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…

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…

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

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…

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.

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

Canonical completion and duality for cylindric ortholattices and cylindric Boolean algebras
Joseph McDonald
https://arxiv.org/abs/2507.17715 https://arxiv.…

Canonical completion and duality for cylindric ortholattices and cylindric Boolean algebras
In this note, we investigate the algebraic and topological representation theory of cylindric ortholattices and cylindric Boolean algebras. The first contribution demonstrates that cylindric ortholattices are closed under canonical completions. By equipping a spectral topology to the dual space associated with the canonical completion, we then establish a dual equivalence between the category of cylindric ortholattices and a certain subcategory of the category of spectral spaces. This work buil…

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…

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

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 …

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…

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…

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…

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]:
- On pure monomorphisms and pure epimorphisms in accessible categories
Leonid Positselski

Fundamentals of Lie categories and Yang-Mills theory for multiplicative Ehresmann connections
\v{Z}an Grad
https://arxiv.org/abs/2507.08220 https://…

Fundamentals of Lie categories and Yang-Mills theory for multiplicative Ehresmann connections
The first and shorter part of the thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible differentiable structure. We introduce various examples of Lie categories, examine their differences and similarities with Lie groupoids, and research the notions emerging naturally from the lack of invertibility of arrows. The aim of the second and principal part of …

An operator algebraic approach to fusion category symmetry on the lattice
David E. Evans, Corey Jones
https://arxiv.org/abs/2507.05185 https://

An operator algebraic approach to fusion category symmetry on the lattice
We propose a framework for fusion category symmetry on the (1+1)D lattice in the thermodynamic limit by giving a formal interpretation of SymTFT decompositions. Our approach is based on axiomatizing physical boundary subalgebra of quasi-local observables, and applying ideas from algebraic quantum field theory to derive the expected categorical structures. We show that given a physical boundary subalgebra $B$ of a quasi-local algebra $A$, there is a canonical fusion category $\mathcal{C}$ that a…

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.

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{…

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Jakob Ulmer
https://arxiv.org/abs/2507.15445 https://

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invari…

$p$-adic Fourier theory in families
Andrew Graham, Pol van Hoften, Sean Howe
https://arxiv.org/abs/2507.05374 https://arxiv.org/pdf/2…

$p$-adic Fourier theory in families
We construct Fourier transforms relating functions and distributions on finite height $p$-divisible rigid analytic groups and objects in a dual category of $\mathbb{Z}_p$-local systems with analyticity conditions. Our Fourier transforms are formulated as isomorphisms of solid Hopf algebras over arbitrary small v-stacks, and generalize earlier constructions of Amice and Schneider--Teitelbaum. We also construct compatible integral Fourier transforms for $p$-divisible groups and their dual Tate mo…

Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic
Karthik Ganapathy
https://arxiv.org/abs/2506.15134 https://

Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic
A long-standing open problem in representation stability is whether every finitely generated commutative algebra in the category of strict polynomial functors satisfies the noetherian property. In this paper, we resolve this problem negatively over fields of positive characteristic using ideas from invariant theory. Specifically, we consider the algebra $P$ of polarizations of elementary symmetric polynomials inside the ring of all multisymmetric polynomials in $p \times \infty$ variables. We s…

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

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Generic modules for the category of filtered by standard modules
Raymundo Bautista Ramos, Jes\'us Efr\'en P\'erez Terrazas, Leonardo Salmer\'on Castro

$C_{pq}$-Injective Diagrams and a Combination Theorem for Minimal Models
Soumyadip Thandar
https://arxiv.org/abs/2506.17998 https://a…

$C_{pq}$-Injective Diagrams and a Combination Theorem for Minimal Models
We study diagrams of commutative differential graded algebras (DGAs) over the orbit category $\sO_G$ in the context of equivariant rational homotopy theory. For $G = C_{pq}$ with $p, q$ distinct primes, we give necessary conditions for injectivity. We prove a combination-type result: the equivariant wedge of injective diagrams over $\mathcal{O}_{C_p}$ and $\mathcal{O}_{C_q}$ with retract structure maps yields an injective diagram over $\mathcal{O}_{C_{pq}}$ with a level-wise minimal model. As a…

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

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, …

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…

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

Lie superalgebras in characteristic 2 and mixed characteristic
Pavel Etingof, Serina Hu
https://arxiv.org/abs/2507.17457 https://arxiv.org/pdf/2507.17457…

Lie superalgebras in characteristic 2 and mixed characteristic
We define the notion of a Lie superalgebra over a field $k$ of characteristic $2$ which unifies the two pre-existing ones - $\mathbb{Z}/2$-graded Lie algebras with a squaring map and Lie algebras in the Verlinde category ${\rm Ver}_4^+(k)$, and prove the PBW theorem for this notion. We also do the same for the restricted version. Finally, discuss mixed characteristic deformation theory of such Lie superalgebras (for perfect $k$), introducing and studying a natural lift of our notion of Lie supe…

[2025-07-25 Fri (UTC), no new articles found for math.CT Category Theory]
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[2025-06-25 Wed (UTC), no new articles found for math.CT Category Theory]
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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.

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]:
- Unstable independence from the categorical point of view
Mark Kamsma, Ji\v{r}\'i Rosick\'y

Supersymmetric Topological Sigma Models and Doubling Spaces
Daniel M. Halmrast
https://arxiv.org/abs/2507.08181 https://arxiv.org/pdf…

Supersymmetric Topological Sigma Models and Doubling Spaces
Witten's topological B-model on a Calabi-Yau background is known to reproduce, in the open string sector, the derived category of coherent sheaves. When the target space is a complex torus, the topological model enjoys a non-geometric symmetry known as T-duality, which relates the theories on the torus and dual torus backgrounds. By considering the "double field theory" of Hull and Reid-Edwards on the product of a torus and its dual, T-duality occurs as a geometric symmetry of the target space.…

Nesting behind $\hat{Z}$-invariants
Shoma Sugimoto
https://arxiv.org/abs/2507.13996 https://arxiv.org/pdf/2507.13996

Nesting behind $\hat{Z}$-invariants
In the spirit of arXiv:2501.12985, we propose an abelian categorification of $\hat{Z}$-invariants for negative definite plumbed 3-manifolds. It provides a blueprint for the expected dictionary between these $3$-manifolds and log VOAs; that is, the contribution from 3d $\mathcal{N}=2$ theory via 3d-3d correspondence is recursively binary encoded in the abelian category of modules over the hypothetical log VOA, and is decoded by the recursive application of the theory of Feigin--Tipunin construct…

Generalised Orbifolds and G-equivariantisation
Sebastian Heinrich, Julia Plavnik, Ingo Runkel, Abigail Watkins
https://arxiv.org/abs/2506.08154 https://

Generalised Orbifolds and G-equivariantisation
In a construction motivated by topological field theory, a so-called orbifold datum $\mathbb{A}$ in a ribbon category $C$ allows one to define a new ribbon category $C_{\mathbb{A}}$. If $C$ is the neutral component of a $G$-crossed ribbon category $B$, and $\mathbb{A}$ is an orbifold datum in $C$ defined in terms of $B$, one finds that $C_{\mathbb{A}}$ is equivalent to the equivariantisation $B^G$ of $B$ as a ribbon category. We give a constructive proof of this equivalence.

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…

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]:
- Representations over diagrams of abelian categories II: Abelian model structures
Zhenxing Di, Liping Li, Li Liang, Nina Yu

Is Crane--Yetter fully extended?
Luuk Stehouwer
https://arxiv.org/abs/2506.04864 https://arxiv.org/pdf/2506.04864

Is Crane--Yetter fully extended?
We revisit the question of whether the Crane-Yetter topological quantum field theory (TQFT) associated to a modular tensor category admits a fully extended refinement. More specifically, we use tools from stable homotopy theory to classify extensions of invertible four-dimensional TQFTs to theories valued in symmetric monoidal 4-categories whose Picard spectrum has nontrivial homotopy only in degrees 0 and 4. We show that such extensions are classified by two pieces of data: an equivalence clas…

[2025-07-24 Thu (UTC), no new articles found for math.CT Category Theory]
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[2025-06-24 Tue (UTC), no new articles found for math.CT Category Theory]
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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…

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)

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}^…

[2025-07-23 Wed (UTC), 1 new article found for math.CT Category Theory]
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[2025-06-23 Mon (UTC), no new articles found for math.CT Category Theory]
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Bousfield-Kan completion as a codensity $\infty$-monad
Emmanuel Dror Farjoun, Sergei O. Ivanov
https://arxiv.org/abs/2507.08414 https://

Bousfield-Kan completion as a codensity $\infty$-monad
We develop a theory of codensity monads associated with full subcategories in the setting of $\infty$-categories. For an $\infty$-monad $\mathcal{M}$ on an $\infty$-category $\mathcal{C}$ that admits homotopy totalizations, we consider the $\mathcal{M}$-completion functor defined as the homotopy totalization of the canonical cosimplicial functor associated with $\mathcal{M}$. We prove that the $\mathcal{M}$-completion is the codensity $\infty$-monad of a full subcategory $\mathcal{A}(\mathcal{M…

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

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.

[2025-07-22 Tue (UTC), 3 new articles found for math.CT Category Theory]
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Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Rewriting techniques for relative coherence
Samuel Mimram

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.

[2025-07-21 Mon (UTC), 1 new article found for math.CT Category Theory]
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[2025-06-20 Fri (UTC), no new articles found for math.CT Category Theory]
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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]:
Are chain-complete posets co-wellpowered?
https://

[2025-06-19 Thu (UTC), no new articles found for math.CT Category Theory]
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Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- On t-structures adjacent and orthogonal to weight structures
Mikhail V. Bondarko

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

[2025-07-18 Fri (UTC), 1 new article found for math.CT Category Theory]
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[2025-06-18 Wed (UTC), 2 new articles found for math.CT Category Theory]
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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…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- On the quotient of a groupoid by an action of a 2-group
Vladimir Drinfeld

[2025-07-17 Thu (UTC), 1 new article found for math.CT Category Theory]
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[2025-06-17 Tue (UTC), 5 new articles found for math.CT Category Theory]
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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…

[2025-07-16 Wed (UTC), no new articles found for math.CT Category Theory]
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[2025-06-16 Mon (UTC), no new articles found for math.CT Category Theory]
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Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Lifting of locally initial objects and universal (co)acting Hopf algebras
Ana Agore, Alexey Gordienko, Joost Vercruysse

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Computation of Smyth and Hoare Power Constructions in Well-filtered Dcpos
Huijun Hou, Qingguo Li

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…

[2025-07-14 Mon (UTC), no new articles found for math.CT Category Theory]
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Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Naive co-contra correspondence for $\mathcal D$-modules
Leonid Positselski

Horizontal Descent, Immersions, Unramified Morphisms, Submersions, \'Etale Morphisms and the Relative Cotangent Sequence in Tangent Categories
Jean-Simon Pacaud Lemay, Geoff Vooys
https://arxiv.org/abs/2506.07874

Horizontal Descent, Immersions, Unramified Morphisms, Submersions, Étale Morphisms and the Relative Cotangent Sequence in Tangent Categories
In this paper we provide a deep and systematic study of the classes of what it means to be an immersion, a submersion, a local diffeomorphism, and unramified in a tangent category. We also give a systematic study of the ways in which these classes of morphisms interact, the properties they have, and give very explicit and concrete characterizations of how each class of maps appear in algebraic geometry, in differential geometry, in the theory of semirings, and in the theory of Cartesian differe…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Higher-dimensional generalization of abelian categories via DG-categories
Nao Mochizuki

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)

This https://arxiv.org/abs/2504.20606 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Monoidal Relative Categories Model Monoidal $\infty$-Categories
We show that the homotopy theory of monoidal relative categories is equivalent to that of monoidal $\infty$-categories, as well as its symmetric monoidal version. As an application, we give a concise and complete proof of the fact that every presentably monoidal or presentably symmetric monoidal $\infty$-category is presented by a monoidal or symmetric monoidal model category, which, in the monoidal case, was sketched by Lurie, and in the symmetric monoidal case, was proved by Nikolaus--Sagave.

[2025-07-11 Fri (UTC), 3 new articles found for math.CT Category Theory]
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[2025-06-11 Wed (UTC), 1 new article found for math.CT Category Theory]
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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…

[2025-07-10 Thu (UTC), no new articles found for math.CT Category Theory]
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[2025-06-10 Tue (UTC), 2 new articles found for math.CT Category Theory]
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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…

[2025-07-09 Wed (UTC), 2 new articles found for math.CT Category Theory]
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[2025-06-09 Mon (UTC), 1 new article found for math.CT Category Theory]
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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/2405.06912 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A simple model for twisted arrow $\infty$-categories
Twisted arrow $\infty$-categories of $(\infty,1)$-categories were introduced by Lurie, and they have various applications in higher category theory. Abellán García and Stern gave a generalization to twisted arrow $\infty$-categories of $(\infty,2)$-categories. In this paper we introduce another simple model for twisted arrow $\infty$-categories of $(\infty,2)$-categories.

[2025-07-08 Tue (UTC), 3 new articles found for math.CT Category Theory]
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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…

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

[2025-06-06 Fri (UTC), 1 new article found for math.CT Category Theory]
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[2025-06-05 Thu (UTC), no new articles found for math.CT Category Theory]
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