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) $\mathrm{C}^*$-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal tensor product, which generalizes that of $\mathrm{C}^*$-algebras, together with the Ghez-Lima-Roberts $\mathrm{C}^*$-categories of *-functors, $\mathrm{C}^*(A;B)$, providing the internal Hom’s.