2023/05/18 by Arthur Pander Maat, Maat, Arthur Pander
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2305.10859
openalex publication_date 2023/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hilbert modules over a C^*-category were first defined by Mitchener, who 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 and characterize equivalences of categories of Hilbert modules as being given by tensoring with imprimitivity bimodules. We employ our results to prove several equivalences of bicategories of C^*-algebras and C^*-categories, and to exhibit a Morita localization of the category of locally small C^*-categories.