Structure of Ann-categories

Abstract

Each Ann-category $\A$ is equivalent to an Ann-category of the type $(R,M),$ where $M$ is an $R$-bimodule. The family of constraints of $A$ induces a {\it structure} on $(R,M).$ The main result of the paper is: 1. {\it There exists a bijection between the set of structures on $(R,M)$ and the group of Mac Lane 3-cocycles $Z_{MaL}^3(R,M).$} 2. {\it There exists a bijection between $C(R,M)$ of congruence classes of Ann-categories whose pre-stick is of the type $(R,M)$ and the Mac Lane cohomology group $H_{\text{MaL}}^3(R,M).$}

This paper has been withdrawn by the author due to has been replaced by the paper arXiv1105.5187

References in corpus (2)

• Introduction to Ann-categories
• On the Axiomatics of Ann-Categories

Cited by in corpus (2)

• Stacks of Ann-Categories and their morphisms
• On the categorical interpretation of ring cohomology