Third Mac Lane cohomology via categorical rings
Mamuka Jibladze, Teimuraz Pirashvili
TL;DR
This paper establishes a classification of categorical rings using third Mac Lane cohomology, linking algebraic structures with cohomological invariants.
Contribution
It demonstrates that the third Mac Lane cohomology group classifies categorical rings with specified object and automorphism structures.
Findings
Third Mac Lane cohomology classifies categorical rings.
Provides a cohomological characterization of categorical rings.
Connects algebraic and categorical structures through cohomology.
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.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Algebraic structures and combinatorial models