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arXiv · 0804.1820

Structure of Ann-Categories

Nguyen Tien Quang
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Abstract

This paper presents the structure conversion by which from an Ann-category $\A,$ we can obtain its reduced Ann-category of the type $(R,M)$ whose structure is a family of five functions $k=(ξ,η,α,λ,ρ)$. Then we will show that each Ann-category is determined by three invariants: 1. The ring $Π_0(\A)$ of the isomorphic classes of objects of $\A$, 2. $Π_0(\A)$-bimodule $Π_1(\A) = \Aut_{\A}(0),$ 3. The element $ \bar{k}\in H^{3}_{M}(Π_0(\A), Π_1(\A))$ (the ring cohomology due to MacLane).

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Nguyen Tien Quang. 2013-09-15. Structure of Ann-Categories. https://arxiv.org/abs/0804.1820

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