Category Theory

Authors and titles for June 2024

[1] arXiv:2406.00223 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Map monoidales and duoidal $\infty$-categories Show Chinese title

Title: 单同态幕和双幕$\infty$-范畴

Takeshi Torii

Comments: 35 pages

Subjects: Category Theory (math.CT) ; Algebraic Topology (math.AT)

[2] arXiv:2406.00417 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Construct ideal cotorsion pairs by recollement of triangulated categories Show Chinese title

Title: 通过三角范畴的recollement构造理想的挠对

Qikai Wang, Haiyan Zhu

Comments: arXiv admin note: text overlap with arXiv:1501.06810 by other authors

Subjects: Category Theory (math.CT)

[3] arXiv:2406.01106 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Strict refinement property of connected loop-free categories Show Chinese title

Title: 连通无环范畴的严格细化性质

Aly-Bora Ulusoy (Cosynus), Emmanuel Haucourt (Cosynus)

Subjects: Category Theory (math.CT)

[4] arXiv:2406.01490 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Groupoidal and truncated $n$-quasi-categories Show Chinese title

Title: 群oidal 和截断的$n$-准范畴

Victor Brittes

Comments: 28 pages

Subjects: Category Theory (math.CT) ; Algebraic Topology (math.AT)

[5] arXiv:2406.01573 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: A classifying localic category for locally compact locales with application to the Axiom of Infinity (poster) Show Chinese title

Title: 局部拓扑范畴的分类及其在无限公理中的应用（海报）

Christopher Francis Townsend

Subjects: Category Theory (math.CT)

[6] arXiv:2406.02788 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Existentially closed models and locally zero-dimensional toposes Show Chinese title

Title: 存在闭模型和局部零维到范畴

Mark Kamsma, Joshua Wrigley

Comments: 30 pages

Subjects: Category Theory (math.CT) ; Logic (math.LO)

[7] arXiv:2406.03969 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: The smashing spectrum of sheaves Show Chinese title

Title: 层的 smash 谱

Ko Aoki

Comments: 9 pages

Subjects: Category Theory (math.CT) ; Commutative Algebra (math.AC) ; Algebraic Topology (math.AT)

[8] arXiv:2406.05425 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Categorical Theory of $(\infty,ω)$-Categories Show Chinese title

Title: 范畴理论的$(\infty,ω)$-范畴

Félix Loubaton

Comments: 239 pages, comments are welcome! This text is based on the author's thesis. arXiv admin note: substantial text overlap with arXiv:2307.11931

Subjects: Category Theory (math.CT)

[9] arXiv:2406.08240 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: On categories with arbitrary 2-cell structures Show Chinese title

Title: 关于具有任意2-单元结构的范畴

Nelson Martins-Ferreira

Comments: 17 pages

Subjects: Category Theory (math.CT)

[10] arXiv:2406.08286 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Copy-composition for Probabilistic Graphical Models Show Chinese title

Title: 概率图模型的复制组合

Toby St Clere Smithe (Verses AI)

Comments: In Proceedings ACT 2024, arXiv:2509.18357

Journal-ref: EPTCS 429, 2025, pp. 146-173

Subjects: Category Theory (math.CT) ; Statistics Theory (math.ST)

[11] arXiv:2406.08925 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: The higher algebra of weighted colimits Show Chinese title

Title: 加权余极限的高阶代数

Hadrian Heine

Subjects: Category Theory (math.CT) ; Algebraic Topology (math.AT)

[12] arXiv:2406.09832 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: On bi-enriched $\infty$-categories Show Chinese title

Title: 关于双富足的$\infty$-范畴

Hadrian Heine

Comments: arXiv admin note: substantial text overlap with arXiv:2406.08925

Subjects: Category Theory (math.CT) ; Algebraic Topology (math.AT)

[13] arXiv:2406.10071 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Right-preordered groups from a categorical perspective Show Chinese title

Title: 从范畴论的角度看右序群

Maria Manuel Clementino, Andrea Montoli

Subjects: Category Theory (math.CT)

[14] arXiv:2406.10624 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Enriched aspects of calculus of relations and $2$-permutability Show Chinese title

Title: 关系微积分的丰富方面和$2$-可交换性

Maria Manuel Clementino, Diana Rodelo

Subjects: Category Theory (math.CT)

[15] arXiv:2406.11076 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Bundles of metric structures as left ultrafunctors Show Chinese title

Title: 度量结构的束作为左超函子

Ali Hamad

Comments: Second version, fixed typos and clarified some proofs

Subjects: Category Theory (math.CT) ; Functional Analysis (math.FA) ; Logic (math.LO)

[16] arXiv:2406.12127 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Invertible cells in $ω$-categories Show Chinese title

Title: 可逆单元在$ω$-范畴中

Thibaut Benjamin, Ioannis Markakis

Subjects: Category Theory (math.CT) ; Logic in Computer Science (cs.LO)

[17] arXiv:2406.12617 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Enriched concepts of regular logic Show Chinese title

Title: 丰富化的正则逻辑概念

Jiří Rosický, Giacomo Tendas

Comments: Final journal version

Subjects: Category Theory (math.CT)

[18] arXiv:2406.13240 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: $ω$-weak equivalences between weak $ω$-categories Show Chinese title

Title: $ω$-范畴之间的弱等价$ω$-范畴

Soichiro Fujii, Keisuke Hoshino, Yuki Maehara

Comments: 33 pages. Major revision. Comments welcome!

Subjects: Category Theory (math.CT)

[19] arXiv:2406.13398 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Non-additive derived functors via chain resolutions Show Chinese title

Title: 非加法通过链分解的函子

Maxime Culot, Fara Renaud, Tim Van der Linden

Comments: 45 pages; final version, accepted for publication

Journal-ref: Glasgow Math. J. 67 (2025) 423-466

Subjects: Category Theory (math.CT)

[20] arXiv:2406.13647 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Inner automorphisms as 2-cells Show Chinese title

Title: 内自同构作为2-单元

Pieter Hofstra, Martti Karvonen

Journal-ref: Theory and Applications of Categories, Vol. 42, No. 2, 2024, pp. 19-40

Subjects: Category Theory (math.CT)

[21] arXiv:2406.14346 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Atomic Toposes with Co-Well-Founded Categories of Atoms Show Chinese title

Title: 原子到poses与原子的共良基范畴

Jérémie Marquès

Comments: Earlier version of a paper published in Theory and Applications of Categories. This version includes some comments on Fra\"iss\'e limits

Subjects: Category Theory (math.CT) ; Logic (math.LO)

[22] arXiv:2406.15137 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: A Tangent Category Perspective on Connections in Algebraic Geometry Show Chinese title

Title: 切线范畴视角下的代数几何中的联络

G.S.H. Cruttwell, Jean-Simon Pacaud Lemay, Elias Vandenberg

Comments: Minor changes and typos fixes based on reviewer comments

Subjects: Category Theory (math.CT)

[23] arXiv:2406.15256 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: Pushforward monads Show Chinese title

Title: 前推单子

Adrián Doña Mateo

Comments: 27 pages

Subjects: Category Theory (math.CT) ; Commutative Algebra (math.AC)

[24] arXiv:2406.15584 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: On the Multicategorical Meta-Theorem and the Completeness of Restricted Algebraic Deduction Systems Show Chinese title

Title: 关于多类别元定理和受限代数演绎系统的完备性

David Forsman

Comments: 30 pages

Subjects: Category Theory (math.CT) ; Logic (math.LO)

[25] arXiv:2406.15884 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: $\mathrm{LMod}_{R}(\mathcal{V})$-enriched $\infty$-categories are left $R$-module objects of $\mathcal{C}at^{\mathcal{V}}$ and $\mathcal{C}at^{\mathcal{V}}$-enriched $\infty$-functors Show Chinese title

Title: $\mathrm{LMod}_{R}(\mathcal{V})$-丰富的$\infty$-范畴是$\mathcal{C}at^{\mathcal{V}}$的左$R$-模对象和$\mathcal{C}at^{\mathcal{V}}$-丰富的$\infty$-函子

Matteo Doni

Comments: In Theorem 6.1, R must be E2 instead of E1. The above error also affects Corollary 6.3, making it incorrect as well

Subjects: Category Theory (math.CT)

[26] arXiv:2406.15887 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: $R\text{-}\mathrm{Mod}$-enriched categories are left $\underline{R}$-module objects of $Cat(\mathbb{A}\mathrm{b})$ and $Cat(\mathbb{A}\mathrm{b})$-enriched functors Show Chinese title

Title: $R\text{-}\mathrm{Mod}$-丰富的范畴是$\underline{R}$-模对象的$Cat(\mathbb{A}\mathrm{b})$以及$Cat(\mathbb{A}\mathrm{b})$-丰富的函子

Matteo Doni

Subjects: Category Theory (math.CT)

[27] arXiv:2406.15895 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: $k$-linear Morita theory Show Chinese title

Title: $k$-线性Morita理论

Matteo Doni

Subjects: Category Theory (math.CT) ; Commutative Algebra (math.AC) ; Algebraic Geometry (math.AG) ; Algebraic Topology (math.AT)

[28] arXiv:2406.17677 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Lifting of locally initial objects and universal (co)acting Hopf algebras Show Chinese title

Title: 局部初始对象的提升和通用（协）作用的霍普夫代数

Ana Agore, Alexey Gordienko, Joost Vercruysse

Comments: 50 pages; final version, to appear in Advances in Mathematics

Subjects: Category Theory (math.CT) ; Quantum Algebra (math.QA) ; Rings and Algebras (math.RA)

[29] arXiv:2406.17684 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Dualities for universal (co)acting Hopf monoids Show Chinese title

Title: 通用（协）作用霍普夫单子的对偶性

Ana Agore, Alexey Gordienko, Joost Vercruysse

Comments: 49 pages; minor changes

Subjects: Category Theory (math.CT) ; Quantum Algebra (math.QA) ; Rings and Algebras (math.RA)

[30] arXiv:2406.18399 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: Kan extendable subcategories and fibrewise topology Show Chinese title

Title: 可扩展子范畴和纤维拓扑

Moncef Ghazel

Comments: 71 pages

Subjects: Category Theory (math.CT)

[31] arXiv:2406.19409 (cross-list from math.CT) [cn-pdf, pdf, html, other]

Title: A Very Short Introduction to Topos Theory (adapted from Prof. Pettigrew's notes) Show Chinese title

Title: 范畴论的一个简短介绍（改编自Pettigrew教授的笔记）

Eric Schmid

Comments: 37 pages

Subjects: Category Theory (math.CT)

[32] arXiv:2406.19816 (cross-list from math.CT) [cn-pdf, pdf, other]

Title: String Diagrams for Physical Duoidal Categories Show Chinese title

Title: 物理双oidal范畴的字符串图

Mario Román

Comments: 26 pages, 11 figures. The author thanks Nayan Rajesh for pointing out a mistake on a previous version of Definition 8.4

Subjects: Category Theory (math.CT)

[33] arXiv:2406.00136 (cross-list from math.AT) [cn-pdf, pdf, other]

Title: Profinite completions of products Show Chinese title

Title: 有限群完成的乘积

Peter J. Haine

Comments: Comments very welcome. 13 pages. A version of this note originally appeared on the author's website in November 2022

Subjects: Algebraic Topology (math.AT) ; Category Theory (math.CT)

[34] arXiv:2406.00161 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: Normed modules and The Stieltjes integrations of functions defined on finite-dimensional algebras Show Chinese title

Title: 赋范模和定义在有限维代数上的Stieltjes积分

Hanpeng Gao, Shengda Liu, Yu-Zhe Liu, Yucheng Wang

Comments: 23 pages

Subjects: Classical Analysis and ODEs (math.CA) ; Category Theory (math.CT)

[35] arXiv:2406.01816 (cross-list from math-ph) [cn-pdf, pdf, other]

Title: Categories of quantum cpos Show Chinese title

Title: 量子cpos的类别

Andre Kornell, Bert Lindenhovius, Michael Mislove

Comments: 80 pages

Subjects: Mathematical Physics (math-ph) ; Logic in Computer Science (cs.LO) ; Category Theory (math.CT) ; Operator Algebras (math.OA) ; Quantum Physics (quant-ph)

[36] arXiv:2406.02194 (cross-list from math.AT) [cn-pdf, pdf, html, other]

Title: A simple characterization of Quillen adjunctions Show Chinese title

Title: Quillen伴随关系的简单特征描述

Victor Carmona

Comments: Comments are welcome!

Subjects: Algebraic Topology (math.AT) ; Category Theory (math.CT)

[37] arXiv:2406.02725 (cross-list from math.SG) [cn-pdf, pdf, html, other]

Title: Non-linear microlocal cut-off functors Show Chinese title

Title: 非线性微局部截断函子

Bingyu Zhang

Comments: v2: 17 pages. Final version to appear in Rend. Sem. Mat. Univ. Padova. Some discussion on the Omega-lens definition of microsupport and requirement on the coefficient are added

Subjects: Symplectic Geometry (math.SG) ; Algebraic Geometry (math.AG) ; Algebraic Topology (math.AT) ; Category Theory (math.CT)

[38] arXiv:2406.02777 (cross-list from math.AT) [cn-pdf, pdf, other]

Title: Spectral sequences via linear presheaves Show Chinese title

Title: 通过线性预层的谱序列

Muriel Livernet, Sarah Whitehouse

Comments: 46 pages

Subjects: Algebraic Topology (math.AT) ; Category Theory (math.CT)

[39] arXiv:2406.02829 (cross-list from math.LO) [cn-pdf, pdf, html, other]

Title: Approximation properties of torsion classes Show Chinese title

Title: 挠类的逼近性质

Sean Cox, Alejandro Poveda, Jan Trlifaj

Subjects: Logic (math.LO) ; Commutative Algebra (math.AC) ; Category Theory (math.CT) ; Rings and Algebras (math.RA)

[40] arXiv:2406.03578 (cross-list from cs.LO) [cn-pdf, pdf, html, other]

Title: Two-dimensional Kripke Semantics II: Stability and Completeness Show Chinese title

Title: 二维克里普克语义 II：稳定性与完备性

G. A. Kavvos

Comments: Accepted at MFPS 2024

Journal-ref: Electronic Notes in Theoretical Informatics and Computer Science, Volume 4 - Proceedings of MFPS XL (December 11, 2024) entics:14767

Subjects: Logic in Computer Science (cs.LO) ; Category Theory (math.CT) ; Logic (math.LO)

[41] arXiv:2406.04965 (cross-list from math.LO) [cn-pdf, pdf, html, other]

Title: Gabriel-Ulmer Duality for Topoi, An Introduction Show Chinese title

Title: 格布里埃尔-乌尔默对偶性，范畴论导论

Federica Pasqualone

Subjects: Logic (math.LO) ; Category Theory (math.CT)

[42] arXiv:2406.05818 (cross-list from math.LO) [cn-pdf, pdf, html, other]

Title: Oracle modalities Show Chinese title

Title: Oracle 模态

Andrew W Swan

Subjects: Logic (math.LO) ; Logic in Computer Science (cs.LO) ; Category Theory (math.CT)

[43] arXiv:2406.07216 (cross-list from cs.LO) [cn-pdf, pdf, html, other]

Title: The Semantics of Effects: Centrality, Quantum Control and Reversible Recursion Show Chinese title

Title: 效果的语义：中心性、量子控制和可逆递归

Louis Lemonnier

Comments: PhD thesis from Universit\'e Paris-Saclay

Subjects: Logic in Computer Science (cs.LO) ; Programming Languages (cs.PL) ; Category Theory (math.CT)

[44] arXiv:2406.07577 (cross-list from cs.AI) [cn-pdf, pdf, html, other]

Title: Structured Active Inference (Extended Abstract) Show Chinese title

Title: 结构化主动推理（扩展摘要）

Toby St Clere Smithe

Subjects: Artificial Intelligence (cs.AI) ; Category Theory (math.CT)

[45] arXiv:2406.08956 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Skein Categories in Non-semisimple Settings Show Chinese title

Title: 非半单设置中的辫群范畴

Jennifer Brown, Benjamin Haïoun

Comments: 29 pages. Comments welcome!

Subjects: Quantum Algebra (math.QA) ; Category Theory (math.CT) ; Geometric Topology (math.GT)

[46] arXiv:2406.08971 (cross-list from math.RT) [cn-pdf, pdf, other]

Title: The index in $d$-exact categories Show Chinese title

Title: $d$-精确范畴中的指标

Francesca Fedele, Peter Jørgensen, Amit Shah

Comments: 18 pages. Final version to appear in Journal of Algebra

Journal-ref: Journal of Algebra, Volume 686, 2026, Pages 814-835

Subjects: Representation Theory (math.RT) ; Category Theory (math.CT)

[47] arXiv:2406.09109 (cross-list from math.RA) [cn-pdf, pdf, other]

Title: Projection algebras and free projection- and idempotent-generated regular $*$-semigroups Show Chinese title

Title: 投影代数和由投影和幂等元生成的正则$*$-半群

James East, Robert D. Gray, P.A. Azeef Muhammed, Nik Ruškuc

Comments: 48 pages, 7 figures, 4 tables. V2: incorporates referee's feedback, to appear in Adv Math

Subjects: Rings and Algebras (math.RA) ; Category Theory (math.CT) ; Group Theory (math.GR)

[48] arXiv:2406.10009 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: Matched pairs and Yetter-Drinfeld braces Show Chinese title

Title: 匹配对和Yetter-Drinfeld括号

Davide Ferri, Andrea Sciandra

Comments: 29 pages; Minor corrections on Definition 4.1 and Theorem 4.3 and other minor adjustments

Subjects: Quantum Algebra (math.QA) ; Category Theory (math.CT) ; Rings and Algebras (math.RA) ; Representation Theory (math.RT)

[49] arXiv:2406.11154 (cross-list from math.AT) [cn-pdf, pdf, other]

Title: Fuzzy simplicial sets and their application to geometric data analysis Show Chinese title

Title: 模糊单纯集及其在几何数据分析中的应用

Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck, Thomas Jan Mikhail

Subjects: Algebraic Topology (math.AT) ; Category Theory (math.CT) ; Metric Geometry (math.MG)

[50] arXiv:2406.11221 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: Symmetric monoidal categories of conveniently-constructible Banach bundles Show Chinese title

Title: 可方便构造的巴拿赫丛的对称单子范畴

Alexandru Chirvasitu

Comments: 22 pages + references; v2 corrects typos and makes small style changes

Subjects: Functional Analysis (math.FA) ; Category Theory (math.CT) ; General Topology (math.GN) ; Operator Algebras (math.OA) ; Rings and Algebras (math.RA)