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

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.

Minor changes, mostly to the Introduction. Corresponds to published version. 18 pages