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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 structure on (R, M). The main result of the paper is: 1. There exists a bijection between the set of structures on (R, M) and the group of Mac Lane 3-cocycles Z 3 MaL(R,M). 2. 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 3 MaL(R, M). 2000 Mathematics Subject Classification:18D10,16E4

Topics:
Ann-category, cohomology, congruence, constraint, monoidal category

Year: 2009

OAI identifier:
oai:CiteSeerX.psu:10.1.1.312.3442

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CiteSeerX

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