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

TL;DR

This paper establishes a new model category framework for small unital C*-categories, using the maximal tensor product and unitary equivalences, advancing the mathematical understanding of C*-categories.

Contribution

It introduces a cofibrantly generated simplicial symmetric monoidal model structure for small unital C*-categories, generalizing existing structures for C*-algebras.

Findings

Defines weak equivalences as unitary equivalences.

Constructs a symmetric monoidal model structure with maximal tensor product.

Provides internal Homs via C*(A,B) 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.