STRUCTURE OF ANN-CATEGORIES AND MAC LANE-SHUKLA COHOMOLOGY

Abstract

In this paper we study the structure of a class of categories having two operations which satisfy axioms analoguos to that of rings. Such categories are called ”Ann-categories”. We obtain the classification theorems for regular Ann-categories and Ann-functors by using Mac Lane-Shukla cohomology of rings. These results give new interpretations of the cohomology groups H3(R,M) andH2(R,M) of the rings R.