Structure of Ann-categories
نویسنده
چکیده
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 Π0(A) of the isomorphic classes of objects of A, 2. Π0(A)-bimodule Π1(A) = AutA(0), 3. The element k̄ ∈ H M (Π0(A),Π1(A)) (the ring cohomology due to MacLane).
منابع مشابه
1 Introduction to Ann − categories
In this paper, we present new concepts of Ann-categories, Ann-functors, and a transmission of the structure of categories based on Ann-equivalences. We build Ann-category End(A) of Pic-funtors F : A −→ A′ and prove that each Ann-category can be faithfully embedded into an almost strictly Ann-category.
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