Ebook: Extension theories for categories (preliminary report)

USA.: Department of Mathematics. Case Western Reserve University. Cleveland. February 7, 2001. P.p.: 1-20, English.
This paper is a slight revision of a paper I wrote in 1980 and never submitted for publication. I would greatly appreciate any information about more recent work on this topic.Abstract.
Let C and A be categories and P: C - A a functor which is bijective on objects and surjective on arrows; then C is an extension of A. This notion of extension is studied here from the point of view of classifying and synthesizing extensions, by generalizing methods used in studying extensions of groups and semigroups. (Functors which merge objects don't behave so much like homomorphisms and probably require intrinsically categorical methods to study them.) More speci cally, in this paper I describe how to study certain extensions of small categories by a method which is essentially the Eilenberg-Mac Lane theory of group extensions in a more general setting.Contents.
Introduction.
Green's relations and Leech's categories.
Extensions.
H-extensions.
Classi cation of extensions by cohomology.
References.