A Quillen model for classical Morita theory and a tensor categorification of the Brauer group

Published 10 Nov 2012 in math.CT and math.RA | (1211.2309v2)

Abstract: Let K be a commutative ring. In this article we construct a symmetric monoidal Quillen model structure on the category of small K-categories which enhances classical Morita theory. We then use it in order to obtain a natural tensor categorification of the Brauer group and of its functoriality.

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