Third Mac Lane cohomology via categorical rings

Abstract

It is proved that the third Mac Lane cohomology group of a ring R with coefficients in a bimodule B classifies categorical rings having R as the ring of isomorphism classes of objects and B as the bimodule of automorphisms of the neutral object.

References in corpus (1)

• Shukla cohomology and additive track theories

Cited by in corpus (17)

• On the Axiomatics of Ann-Categories
• On abelian 2-categories and derived 2-functors
• Stacks of Ann-Categories and their morphisms
• Enrichments over symmetric Picard categories
• Projective and injective objects in symmetric categorical groups
• Higher Dimensional Homology Algebra II:Projectivity
• Cohomological Classification of Ann-categories
• Cohomological classification of Ann-functors
• Biextensions, bimonoidal functors, multilinear functor calculus, and categorical rings
• On monoidal equivalences and Ann-equivalences
• Categorical rings subsume ann-categories
• On a notion of ring groupoid
• 2-Modules and the Representation of 2-Rings
• Abelian categories in dimension 2
• Cohomological classification of braided $Ann$-categories
• On the categorical interpretation of ring cohomology
• Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)