#
Actions in modified categories of interest with application to crossed modules

##
Y. Boyaci, J. M. Casas, T. Datuashvili and E. O. Uslu

The existence of the split extension classifier of a crossed module in the
category of associative algebras is investigated. According to the equivalence
of categories $XAss \simeq Cat^1-Ass$ we consider this problem in $Cat^1-Ass$.
This category is not a category of interest, it satisfies its all axioms except
one. The action theory developed in the category of interest is adapted to the
new type of category, which will be called modified category of interest.
Applying the results obtained in this direction and the equivalence of
categories we find a condition under which there exists the split extension
classifier of a crossed module and give the corresponding construction.

Keywords:
split extension classifier, category of interest, associative algebra, crossed
module, cat^1-associative algebra, equivalence of categories, actor, universal
strict general actor, bimultiplier

2010 MSC:
08A99, 08C05, 16E99, 18B99

*Theory and Applications of Categories,*
Vol. 30, 2015,
No. 25, pp 882-908.

Published 2015-06-30.

http://www.tac.mta.ca/tac/volumes/30/25/30-25.pdf

Revised 2016-06-20. Original version at

http://www.tac.mta.ca/tac/volumes/30/25/30-25a.pdf

TAC Home