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Tensor structure on kC-mod and cohomology

Part of: Categories with structure Homological methods

Published online by Cambridge University Press:  05 December 2012

Fei Xu
Fei Xu*
Affiliation:
Institut für Mathematik, Universität Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany (feixu@math.upb.de)
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Abstract

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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.

Keywords

category algebraclosed symmetric monoidal categoryordinary cohomology ringHochschild cohomology ringtransporter categoriesfinite generation

MSC classification

Secondary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 349 - 370
Copyright
Copyright © Edinburgh Mathematical Society 2012

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