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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…

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 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…

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…

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…

Locally finitely presented Grothendieck categories with a flat generator
Lorenzo Martini, Carlos E. Parra, Manuel Saor\'in, Simone Virili
https://arxiv.org/abs/2508.00670 ht…

Locally finitely presented Grothendieck categories with a flat generator
A problem raised by Cuadra and Simson in 2007 asks whether a locally finitely presented Grothendieck category with enough flat objects has enough projective objects. We prove that the categories involved in the statement are precisely the locally finitely presented Grothendieck categories with exact product functors. This enables reformulations of the problem that answer the latter in the negative and prove that it is related to a classical problem posed by Miller in 1975 and to the Telescope C…

Baues-Wirsching Cohomology and Svarc Genus in Small Categories
Isaac Carcac\'ia-Campos, Enrique Mac\'ias-Virg\'os, David Mosquera-Lois
https://arxiv.org/abs/2508.00727

Baues-Wirsching Cohomology and Svarc Genus in Small Categories
We prove that for a bifibration P between small categories, the lenght of the cup product in the kernel of the induced morphism in the Baues-Wirsching cohomology with coefficients in any natural system is a lower bound for the homotopic sectional category (also called Svarc genus). Our results extend classical Svarc type inequalties to the categorical setting and introduce a computationally efficient method via a reduced cochain complex for Baues-Wirching cohomology.

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/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…

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…