Cohomology of Pointed Finite Tensor Categories
Bowen Li, Gongxiang Liu
TL;DR
This paper investigates the cohomology algebra of pointed finite tensor categories, demonstrating finite generation for categories over abelian groups using de-equivariantization and exact sequences.
Contribution
It establishes finite generation of cohomology for all coradically graded pointed finite tensor categories over abelian groups, advancing understanding in tensor category cohomology.
Findings
Finite generation of cohomology for categories over abelian groups
Application of de-equivariantization techniques
Use of exact sequences in proving finite generation
Abstract
We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a result, we prove that all coradically graded pointed finite tensor categories over abelian groups have finitely generated cohomology.
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Taxonomy
TopicsTensor decomposition and applications · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models