# Gelfand-Naimark for $C^*$-categories

What is a reference for the following Theorem?

If $A$ is a small $C^*$-category, then there is a faithful $C^*$-functor $A \to \mathsf{Hilb}$.

$C^*$-categories with exactly one object are just $C^*$-algebras, and in that case the Theorem coincides with the usual Gelfand-Naimark Theorem.

This is Theorem 6.12 of Paul Mitchener's article $C^\ast$-categories.