Pushouts of profinite crossed modules and $cat^1$ -profinite groups

Abstract

In this paper, we presented a brief review of crossed modules [7], $cat^1$ -groups [6], pullback crossed modules [4], pullback $cat^1$ -group [1], profinite crossed modules [5], $cat^1$ -profinite groups [5], pullback profinite crossed modules [5], pullback $cat^1$ -profinite groups [3]. We defined the pushout $cat^1$ -profinite groups and gave the left adjoint constructions.