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Keywords:
non-unital $C^*$-categories; crossed products; exact sequences
non-unital $C^*$-categories; crossed products; exact sequences
Summary:
We provide a reference for basic categorial properties of the categories of (possibly non-unital) $\mathbb{C}$-linear *-categories or C*-categories, and (not necessarily unit-preserving) functors. Generalizing the classical case of algebras with $G$-action, we extend the construction of crossed products to categories with G-action. We will show that the crossed product functor preserves exact sequences and excisive squares and sends weak equivalences to equivalences.
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