Geodesic
Derivations of categorical groups
Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 86-105

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18D10, 18G50, 20J05, 20L05
Keywords: derivation, categorical group, cohomology 
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A.R. Garzon; H. Inassaridze; A. del Rio. Derivations of categorical groups. Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 86-105. http://geodesic.mathdoc.fr/item/TAC_2004_13_a4/