  By regarding the classical non abelian cohomology of groups from a
2-dimensional categorical viewpoint, we are led to a non abelian cohomology of
groupoids which continues to satisfy classification, interpretation and
representation theorems generalizing the classical ones. This categorical
approach is based on the fact that if groups are regarded as categories, then,
on the one hand, crossed modules are 2-groupoids and, cocycles are lax
2-functors and the cocycle conditions are precisely the coherence axioms for
lax 2-functors, and, on the other hand group extensions are fibrations of
categories. Furthermore, $n$-simplices in the nerve of a 2-category are lax
2-functors.
