Related papers: Strict $\omega$-categories are monadic over polygr…

We prove that $\ omega $-categorical dp-minimal groups are nilpotent-by-finite. We also show that in dp-minimal definably amenable groups, f-generic global types are strongly f-generic.

Motivated by the Grothendieck construction, we study the functorialities of the comma construction for strict $\omega$-categories. To state the most general functorialities, we use the language of Gray $\omega$-categories, that is,…

We show that the nerve of a strict omega-category can be described algebraically as a simplicial set with additional operations subject to certain identities. The resulting structures are called sets with complicial identities. We also…

Extriangulated categories axiomatize extension-closed subcategories of triangulated categories. We show that the homotopy category of an exact quasi-category can be equipped with a natural extriangulated structure.

We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of…

We prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we…

In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle:…

An elementary theory of strict $\infty $-categories with application to concrete duality is given. New examples of first and second order concrete duality are presented.

We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.

We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category $\mathsf{Pos}$ of partially ordered sets. Paralleling the ordinary case, we characterize categories…

The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…

In this paper we study multiplicative structures on comodules over bialgebras in the setting of $\infty$-categories. We show that the $\infty$-category of comodules over an $(\mathcal{O},\mathbf{Ass})$-bialgebra in a mixed…

In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains…

We show that special cycles generate a large part of the cohomology of locally symmetric spaces associated to orthogonal groups. We prove in particular that classes of totally geodesic submanifolds generate the cohomology groups of degree…

We show that, with some technical conditions, an abelian category can be embedded into the category of bimodules over a ring. The case of semisimple rigid monoidal categories is studied in more detail.

The combination of this paper and its companion complete the classification of monodromy groups of indecomposable coverings of complex curves $f:X\rightarrow \mathbb P^1$ of sufficiently large degree in comparison to the genus of $X$. In…

We introduce a notion of fine Tannakian infinity-categories and prove Tannakian characterization results for symmetric monoidal stable infinity-categories over a field of characteristic zero. It connects derived quotient stacks with…

We prove that the folk model structure on strict $\infty$-categories transfers to the category of strict $\infty$-groupoids (and more generally to the category of strict $(\infty, n)$-categories), and that the resulting model structure on…

Classification problems of subcategories have been deeply considered so far. In this paper, we discuss classifying dense (co)resolving subcategories of exact categories via their Grothendieck groups. This study is motivated by the…

We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.