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hochschild cohomology ring

Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Tensor structure on kC-mod and cohomology
Part of
- Categories with structure
- Homological methods
Fei Xu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 1 / February 2013

Published online by Cambridge University Press:

05 December 2012, pp. 349-370
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Let be a finite category and let k be a field. We consider the category algebra and show that -mod is closed symmetric monoidal. Through comparing with a co-commutative bialgebra, we exhibit the similarities and differences between them in terms of homological properties. In particular, we give a module-theoretic approach to the multiplicative structure of the cohomology rings of small categories. As an application, we prove that the Hochschild cohomology rings of a certain type of finite category algebras are finitely generated.