The unitary symmetric monoidal model category of small C*-categories

Abstract

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal tensor product, which generalizes that of C*-algebras, with the Ghez-Lima-Roberts C*-categories of *-functors, C*(A,B), providing the internal Hom's.