Diextensions et panextensions de catégories

Abstract

Considering some different notions of kernel for a quotient functor, news kinds of extensions of (small) categories appear. In each context, one sees how 2-cocycles are naturally defined. Classical 2-cohomologies, like Hochschild's one (for which the need of commutativity is here discussed), are particular cases in this framework. One has thus an unifying point of view for extensions structures.