Related papers: Actor of categories internal to groups

We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures; and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give…

In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…

We decompose the crossed product functor for actions of crossed modules of locally compact groups on C*-algebras into more elementary constructions: taking crossed products by group actions and fibres in C*-algebras over topological spaces.…

There are two major structure theorems for an arbitrary regular semigroup using categories, both due to Nambooripad. The first construction using inductive groupoids departs from the biordered set structure of a given regular semigroup.…

We give explicit axioms for the algebraic theory of the quasivarieties of right-preordered groups and preordered groups. We then look at lattices of effective equivalence relations, which turn out to be similar to the lattices of…

We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided $G$-crossed categories.

We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories.…

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is…

We study a certain type of action of categories on categories and on operads. Using the structure of the categories {\Delta} and {\Omega} governing category and operad structures, respectively, we define categories which instead encode the…

We propose a new model for multicategories with symmetries with respect to Zhang's group operads. The fully faithful embedding of the category of group operads into that of crossed interval groups is made use of, and it is shown that every…

We develop a categorical analogue of Clifford theory for strongly graded rings over graded fusion categories. We describe module categories over a fusion category graded by a group $G$ as induced from module categories over fusion…

Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad…

We introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call,…

In this work we study the notion of Whitehead sequence in the category of crossed modules and actions of crossed modules. As expected, Whitehead sequences in that context are the same as crossed squares. We investigate under which…

We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…

A groupoid is a small category in which all morphisms are isomorphisms. An inductive groupoid is a specialised groupoid whose object set is a regular biordered set and the morphisms admit a partial order. A normal category is a specialised…

This is the second part of the paper. Results of the first part about crossed modules are applied here to study of quantum groups in braided categories. Correct cross product in the class of quantum braided groups is built. Criterion when…

Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in…

In this paper we prove some results on the covering morphisms of internal groupoids. We also give a result on the coverings of the crossed modules of groups with operations.

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category $\mathsf{C}$ of groups with operations using the categorical equivalence between crossed modules and internal categories in…