Cohomological classification of braided $Ann$-categories

Abstract

A braided $Ann$-category $\mathcal A$ is an $Ann$-category $\mathcal A$ together with a braiding $c$ such that $(\mathcal A, \otimes, a, c, (1,l,r))$ is a braided tensor category, moreover $c$ is compatible with the distributivity constraints. According to the structure transport theorem, the paper shows that each braided $Ann$-category is equivalent to a braided $Ann$-category of the type $(R,M)$, hence the proof of the classification theorem for braided $Ann$-categories by the cohomology of commutative rings is presented.