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.

25 pages

References in corpus (2)

• Third Mac Lane cohomology via categorical rings
• Introduction to Ann-categories