Semidirect products of categorical groups. Obstruction theory

Abstract

By considering the notion of action of a categorical group G on another categorical group H we define the semidirect product H G and classify the set of all split extensions of G by H. Then, in an analogous way to the group case, we develop an obstruction theory that allows the classification of all split extensions of categorical groups inducing a given pair (ϕ, ψ) (called a collective character of G in H) where ϕ : π 0 (G) → π 0 (Eq(H)) is a group homomorphism and ψ : π 1 (G) → π 1 (Eq(H)) is a homomorphism of π 0 (G)-modules. This paper has been financially supported by NATO PST.CLG 975316.

Equivariant Extensions of Categorical Groups

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A Decomposition for the Low Dimensional Cohomology of Semidirect Product of Topological Groups

“…1991;Berndt O. 1994] and categorical group [Garzon, A.R., 2001]. In this paper we use it in the category of topological groups.…”

The semidirect product and the first cohomology of topological groups

“…In recent years it has found its way into Banach algebra theory [7,9,3] and categorical group [5].In this paper we use it in the category of topological groups . Spaces are assumed to be completely regular and Hausdorff.…”