A Picard–Brauer exact sequence of categorical groups

Categorical representations of categorical groups

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

On the Second Cohomology Categorical Group and a Hochschild-serre 2-exact Sequence

Résumé. We introduce the second cohomology categorical group of a categorical group G with coefficients in a symmetric G-categorical group and we show that it classifies extensions of G with symmetric kernel and a functorial section. Moreover, from an essentially surjective homomorphism of categorical groups we get 2-exact sequences à la Hochschild-Serre connecting the categorical groups of der...

Soluble omega-categorical groups

Effectively Categorical Abelian Groups

We study effective categoricity of computable abelian groups of the form ⊕ i∈ω H, where H is a subgroup of (Q,+). Such groups are called homogeneous completely decomposable. It is well-known that a homogeneous completely decomposable group is computably categorical if and only if its rank is finite. We study ∆n-categoricity in this class of groups, for n > 1. We introduce a new algebraic concep...