Girard quantaloids

DOI10.1017/S0960129500001146zbMath0761.18008OpenAlexW4248272788MaRDI QIDQ4006239

Kimmo I. Rosenthal

Publication date: 26 September 1992

Published in: Mathematical Structures in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0960129500001146

zbMATH Keywords

quantaloidsGirard quantalescategories enriched in the closed monoidal category of sup-latticescyclic dualizing elementGirard's linear negation

Mathematics Subject Classification ID

Categorical logic, topoi (03G30) Ordered semigroups and monoids (06F05) Enriched categories (over closed or monoidal categories) (18D20)

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\(*\)-autonomous categories of bimodules ⋮ Quantaloids, enriched categories and automata theory ⋮ Fixed points of adjoint functors enriched in a quantaloid ⋮ Autonomous posets and quantales ⋮ On quantaloids and quantal categories ⋮ The Involutive Quantaloid of Completely Distributive Lattices ⋮ Diagonals between \(\mathcal{Q}\)-distributors ⋮ Chu connections and back diagonals between \(\mathcal{Q}\)-distributors ⋮ Unnamed Item ⋮ Regularity vs. constructive complete (co)distributivity ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Involutive and relational quantaloids

Cites Work

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• Order ideals in categories
• Variation through enrichment
• An axiomatics for bicategories of modules
• Quantales and (noncommutative) linear logic
• Applications of Sup-Lattice Enriched Category Theory to Sheaf Theory
• Constructing locales from quantales
• Adjointness in Foundations