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

C*-categories are "C*-algebras with many objects", as they provide an axiomatization of norm-closed *-closed subcategories of bounded operators between Hilbert spaces. Besides (unital) C*-algebras, naturally occurring examples include various categories of representations and Hilbert modules, groupoid C*-categories, the Ghez-Lima-Roberts categories of *-functors, etc. Many of these known constructions, and a few new ones, conspire together to equip the category of all small C*-categories and *-functors with the structure of a simplicial symmetric monoidal Quillen model category. Our model is intimately related to the "folk" models on categories and groupoids; indeed, the weak equivalences are the unitary equivalences: *-functors which are equivalences of the underlying categories, compatibly with the involutions. We will suggest some possible future uses for the unitary model.