Some adjoint pair of covariant functors between the category of profinite crossed modules and some related categories

الملخص EN

In this paper, we introduce and study some adjoint pairs of covariant functors.

The first adjoint pair of covariant functors is constructed between the category of profinite crossed modules and the category of profinite transformation groups, which explains how to construct a profinite crossed module from a given profinite transformation group.

The second adjoint pair of covariant functors is constructed between the category of free profinite crossed modules and the category of continuous maps (from profinite spaces into profinite groups) which explains how to construct a free profinite crossed module on a continuous map from a profinite space into a profinite group