Intrinsic Schreier-Mac Lane extension theorem II: The case of action accessible categories

In (Bourn, 2008 [11], ), the Schreier-Mac Lane extension theorem in the category Gp of groups, which describes a simply transitive group action on a certain indexed class of non-abelian extensions, was extended to any exact pointed protomodular category with split extension classifiers. We show here that the same scheme of proofs allows us to extend it to any exact action accessible category in the sense of Bourn and Janelidze (2009) [13], , which includes the case of any category of interest in the sense of Orzech (1972) [21].