Structure of Ann-categories

Each Ann-category $\text{A}$ 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 $(R,M)\mathrm{.}$ 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 $Z_{MaL}^3(R,M)\mathrm{.}$}
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 $H_{\text{MaL}}^3(R,M)\mathrm{.}$}