Balan, Adriana; Kurz, Alexander An equational approach to enriched distributivity. (English) Zbl 1524.18009 Rev. Roum. Math. Pures Appl. 66, No. 3-4, 577-596 (2021). Summary: The familiar adjunction between ordered sets and completely distributive lattices can be extended to generalised metric spaces, that is, categories enriched over a quantale (a lattice of “truth values”), via an appropriate distributive law between the “down-set” monad and the “up-set” monad on the category of quantale-enriched categories. If the underlying lattice of the quantale is completely distributive, and if powers distribute over non-empty joins in the quantale, then this distributive law can be concretely formulated in terms of operations, equations and choice functions, similar to the familiar distributive law of lattices. MSC: 18B35 Preorders, orders, domains and lattices (viewed as categories) 18C05 Equational categories 06D10 Complete distributivity 18D20 Enriched categories (over closed or monoidal categories) 06F07 Quantales 08A65 Infinitary algebras Keywords:quantale; enriched category; weighted (co)limit; (co)complete enriched category; completely distributive quantale-enriched category PDFBibTeX XMLCite \textit{A. Balan} and \textit{A. Kurz}, Rev. Roum. Math. Pures Appl. 66, No. 3--4, 577--596 (2021; Zbl 1524.18009) Full Text: arXiv Link