Overview
We propose here a study of semiexact homological categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on;Homological Algebra, The interplay of homology with distributive lattices and orthodox semigroups is published by the same Editor, but can be read independently of the latter.