A Quillen model for classical Morita theory and a tensor   categorification of the Brauer group
  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. 
Ivo Dell'Ambrogio, Gon\c{c}alo Tabuada
math.CT math.RA