On the Axiomatics of Ann-Categories

Abstract

In this paper, we have studied the axiomatics of {\it Ann-categories} and {\it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have achieved is proving the independence of the axiomatics of Ann-category definition. And then we have proved that after adding an axiom into the definition of categorical rings, we obtain the new axiomatics which is equivalent to the one of Ann-categories.

arXiv comment13 pages

References in corpus (2)

• Third Mac Lane cohomology via categorical rings
• Introduction to Ann-categories

Cited by in corpus (8)

• On the braiding of an Ann-category
• Stacks of Ann-Categories and their morphisms
• Higher Dimensional Homology Algebra II:Projectivity
• Structure of Ann-categories
• Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings
• Cohomological classification of Ann-functors
• Categorical rings subsume ann-categories
• Abelian categories in dimension 2