2022/05/25 by Alexandru Chirvăsitu, Chirvasitu, Alexandru
Mathematics · Medicine · #18A30 #18C35 #18D15 #18D20 #46L05 #46L09 #51F30 #54E40 #54E50 #Advanced Operator Algebra Research #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Metric Geometry (math.MG) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2205.12666
openalex publication_date 2022/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of intrinsic complete metric spaces is locally ℵ1-presentable, closed monoidal, and comonadic over CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry-ℵ0-generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include the automatic completeness of a colimit of bi-Lipschitz morphisms of complete metric spaces and a characterization of those pairs (metric space, unital C^*-algebra) that have a tensor product in the CMet-enriched category of unital C^*-algebras.