Cohomological classification of Ann-categories
نویسنده
چکیده
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
منابع مشابه
Bundles of C*-categories and duality
We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of C*-categories, with base space the spectrum of the C*-algebra associated with the identity object. We classify tensor C*-categories with fibre the dual of a ...
متن کاملSuspension and Loop Objects and Representability of Tracks
In the general setting of groupoid enriched categories, notions of suspender and looper of a map are introduced, formalizing a generalization of the classical homotopy-theoretic notions of suspension and loop space. The formalism enables subtle analysis of these constructs. In particular, it is shown that the suspender of a principal coaction splits as a coproduct. This result leads to the noti...
متن کاملThe Fiber of Functors between Categories of Algebras
We investigate the fiber of a functor F : C → D between sketchable categories of algebras over an object D ∈ D from two points of view: characterizing its classifying space as a universal Aut(D)-space, and parametrizing its objects in cohomological terms.
متن کاملCohomological Symmetry in Triangulated Categories
We give a criterion for cohomological symmetry in a triangulated category. As an application, we show that such cohomological symmetry holds for all pairs of modules over any exterior algebra.
متن کاملGeometric construction of spinors in orthogonal modular categories
A geometric construction of Z2–graded odd and even orthogonal modular categories is given. Their 0–graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions and twist coefficients of 1–graded simple objects (spinors) are calculated. We show that invariants coming from our odd and even...
متن کامل