| الوصف: |
Hilbert modules over a $C^*$-category were first defined by Mitchener, where it was also proved that they form a $C^*$-category. An Eilenberg-Watts theorem for Hilbert modules over $C^*$-algebras was proved by Blecher. We follow a similar path to prove an Eilenberg-Watts theorem for Hilbert modules over $C^*$-categories, characterize equivalences of categories of Hilbert modules as being given by tensoring with imprimitivity bimodules, and employ our results to prove several equivalences of bicategories of $C^*$-algebras and $C^*$-categories. |
