Structure of Ann-categories

2008/05/11 by Quang, Nguyen Tien
#16E40 #18D10 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.0805.1505

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 Z³_MaL(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 H³_\textrmMaL(R,M).

Related

• Structure of Ann-Categories
• Ring extension problem, Shukla cohomology and Ann-category theory
• Cohomological Classification of Ann-categories
• On the categorical interpretation of ring cohomology
• Third Mac Lane cohomology via categorical rings