#
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.

http://www.tac.mta.ca/tac/volumes/13/5/13-05.dvi

http://www.tac.mta.ca/tac/volumes/13/5/13-05.ps

http://www.tac.mta.ca/tac/volumes/13/5/13-05.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/13/5/13-05.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/13/5/13-05.ps

TAC Home