On the tensor product of completely distributive quantale-enriched categories

2025/01/21 by Adriana Balan, Balan, Adriana
Mathematics · #06D10 #06F07 #18A40 #18B35 #18C20 #18D20 #18M05 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2501.12014

openalex publication_date 2025/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Tensor products are ubiquitous in algebra, topology, logic and category theory. The present paper explores the monoidal structure of the category V\hspace0pt-\hspace.5ptSup of separated cocomplete enriched categories over a commutative quantale V, the many-valued analogue of complete sup-lattices. We recover the known result that V\hspace0pt-\hspace.5ptSup is *-autonomous and we show that the nuclear/dualizable objects in V\hspace0pt-\hspace.5ptSup are precisely the completely distributive cocomplete V-categories.

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