Title: Tensor structure on kC-mod and cohomology

Author: 徐 斐 Xu, Fei

Address: Institut für Mathematik, Universität Paderborn,
Warburger Str. 100, 33098 Paderborn, Germany.

Current address: Departament de Matemàtiques, Universitat
Autònoma de Barcelona, 08193 Bellaterra, Spain; E-mail:
xu@mat.uab.cat

Keywords: Category algebra, closed symmetric monoidal category,
ordinary cohomology ring, Hochschild cohomology ring, transporter
categories, finite generation.

Abstract: Let C be a finite category and k a field. We consider the
category algebra kC and show kC-mod is closed symmetric monoidal.
Through comparing kC with a cocommutative bialgebra, we exhibit the
similarities and differences between them in terms of homological
properties. Especially we give a module-theoretic approach to the
multiplicative structure of the cohomology rings of small
categories. As an application, we prove the Hochschild cohomology
rings of a certain type of finite category algebras are finite
generated.


Status: to appear in Skye 2009 Conference Proceedings.