منابع مشابه
Structure of Ann-categories
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 ...
متن کاملCohomological classification of Ann-categories
An Ann-category is a categorification of rings. Regular Ann-categories were classified by Shukla cohomology of algebras. In this paper, we state and prove the precise theorem on classification of Ann-categories in the general case based on Mac Lane cohomology of rings. AMS subject classifications: 18D10, 16E40
متن کامل1 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.
متن کاملGray Categories with Duals and Their Diagrams
The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a cube, with regions, surfaces, lines and vertices labelled by Gray category data. These can be viewed as a generalisation of ribbon diagrams. The Gray categories present two types of duals, which are extended to functor...
متن کاملThe Relation between Ann-categories and Ring Categories
There are different categorizations of the definition of a ring such as Ann-category [6], ring category [2],... The main result of this paper is to prove that every axiom of the definition of a ring category, without the axiom x0 = y0, can be deduced from the axiomatics of an Ann-category.
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2012
ISSN: 1225-1763
DOI: 10.4134/ckms.2012.27.1.023