Adjunctions between peiffer crossed modules and crossed modules and between commutator cat1-groups and cat1-groups

Abstract EN

The notions of crossed modules and catP1P-groups have been generalized to the notions of peiffer crossed modules and commutator catP1P-groups, respectively.

There are well known two adjunctions between pre-crossed modules and crossed modules over a fixed "base" group, and between pre-catP1P-groups and catP1P-groups, as well.

As a parallel study to the construction of these adjunctions, two new adjunctions have been constructed by using the above generalizations.

One of them is between the categories of peiffer crossed modules and crossed modules over a fixed "top" group, while the other between the categories of commutator catP1P-groups and catP1P-groups, as well.