Third Mac Lane cohomology via categorical rings

2006/08/21 by Mamuka Jibladze, Teimuraz Pirashvili, Jibladze, Mamuka +1 · 6 citations
Mathematics · #16E40 #18G60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.math/0608519

openalex publication_date 2006/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• An alternative description of symmetric monoidal categories, and symmetric 2-groups
• Cohomological classification of braided Ann-categories
• On the categorical interpretation of ring cohomology
• Projective and injective objects in symmetric categorical groups
• Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)
• Cohomological Classification of Ann-categories

Related

• Third Mac Lane cohomology
• Structure of Ann-categories
• The third cohomology group classifies crossed module extensions
• Ring extension problem, Shukla cohomology and Ann-category theory
• Enrichments over symmetric Picard categories