Derivations of categorical groups

A.R. Garzon, H. Inassaridze and A. del Rio

In this paper we introduce and study the categorical group of derivations, Der(G, A), from a categorical group G into a braided categorical group (A,c) equipped with a given coherent left action of G. Categorical groups provide a 2-dimensional vision of groups and so this object is a sort of 0-cohomology at a higher level for categorical groups. We show that the functor Der(-, A) is corepresentable by the semidirect product of A with G and that Der(G,-) preserves homotopy kernels. Well-known cohomology groups, and exact sequences relating these groups, in several different contexts are then obtained as examples of this general theory.

Keywords: derivation, categorical group, cohomology

2000 MSC: 18D10, 18G50, 20J05, 20L05

Theory and Applications of Categories, Vol. 13, 2004, No. 5, pp 86-105.

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