Structure of Ann-categories and Mac Lane - Shukla cohomology

TL;DR

This paper investigates Ann-categories, which are categories with ring-like operations, and uses Mac Lane-Shukla cohomology to classify them, providing new insights into the structure of rings and their cohomology.

Contribution

It introduces classification theorems for regular Ann-categories and functors using Mac Lane-Shukla cohomology, offering novel interpretations of cohomology groups and rings.

Findings

Classification of regular Ann-categories achieved

New interpretations of cohomology groups provided

Connections between Ann-categories and ring cohomology established

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 and of the rings