On Whitehead product of derivations

Non-abelain cohomology of groups is based on the notion of derivation of a group G with values in a G-group H. We provide an analysis of the Whitehead Theorem stating that if H is a G-crossed module, then the set of derivations is a monoid. We revisit this theorem using the fact that crossed modules correspond to internal groupoids in the category of groups, and also to strict categorical groups.