## Andrea Montoli: Semidirect
products and split short five lemma in algebraic categories

N. Martins Ferreira and M. Sobral proved that, in a pointed regular
category C, the split epimorphisms are equivalent to the internal
actions if and only if C is protomodular and every internal action is
strict. We will show that, even if C is not protomodular, the regular
split epimorphisms (i.e. those such that the kernel and the section are
jointly regularly epimorphic) are equivalent to the internal actions if
and only if in C a particular case of split short five lemma holds.

This is a joint work with Nelson Martins Ferreira and Manuela Sobral.