Related papers: Actor of categories internal to groups

We introduce the concept of crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system.…

This paper touches on several interaction points of semigroups and constructions from category theory: An adjunction is established between categories with selected arrows and semigroups. Regular semigroups are characterized by split epi -…

The theory of representations of a crossed module is a direct generalization of the theory of representations of groups. For a finite group G, the Drinfeld quantum double of the group G is a Hopf algebra that represents a special case of…

Prolongations of a group extension can be studied in a more general situation that we call group extensions of the co-type of a crossed module. Cohomology classification of such extensions is obtained by applying the obstruction theory of…

We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples

We introduce generalized Frobenius-Schur indicators for pivotal categories. In a spherical fusion category C, an equivariant indicator of an object in C is defined as a functional on the Grothendieck algebra of the quantum double Z(C) via…

To an inverse semigroup, we associate an \'etale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of this groupoid are non-Hausdorff. We show that…

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…

We describe a pretorsion theory in the category $Cat$ of small categories: the torsion objects are the groupoids, while the torsion-free objects are the skeletal categories, i.e., those categories in which every isomorphism is an…

In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.

The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…

We develop the K-theory of sets with an action of a pointed monoid (or monoid scheme), analogous to the $K$-theory of modules over a ring (or scheme). In order to form localization sequences, we construct the quotient category of a nice…

If $\Gamma $ is a group, then braided $\Gamma $-crossed modules are classified by braided strict $\Gamma $-graded categorial groups. The Schreier theory obtained for $\Gamma $-module extensions of the type of an abelian $\Gamma $-crossed…

We introduce the notion of groupoidal (weak) test category, which is a small category A such that the groupoid-valued presheaves over A models homotopy types in a "canonical and nice" way. The definition does not require a priori that A is…

Given a group action on a finite set, we define the group-action model which consists of tensor network diagrams which are invariant under the group symmetry. In particular, group-action models can be realized as the even part of…

We introduce the notion of $(G, \Gamma)$-crossed action on a tensor category, where $(G, \Gamma)$ is a matched pair of finite groups. A tensor category is called a $(G, \Gamma)$-crossed tensor category if it is endowed with a $(G,…

We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module…

Categorial actions of braided tensor categories are defined and shown to be the right framework for a discussion of the categorial structure related to the group of braids in the cylinder. A Kauffman polynomial of links in the solid torus…

We define the notion of the $(G,\Gamma)$-crossed center of a $(G,\Gamma)$-crossed tensor category in the sense of Natale. We show that the $(G, \Gamma)$-crossed center is a $(G \bowtie \Gamma, G \times \Gamma)$-braided tensor category. This…