Geodesic
Ideals and continuity for quantaloid-enriched categories
Theory and applications of categories, Tome 39 (2023), pp. 687-713.

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We study ideals in, and continuity of, quantaloid-enriched categories (Q-categories for short) as a `many-valued and many-typed' generalization of domain theory. Abstractly, for any (saturated) class Φ of presheaves, we define and study the Φ-continuity of Q-categories. Concretely, we compute three examples of such saturated classes of presheaves - the class of flat ideals, the class of irreducible ideals and the class of conical ideals - which are proper generalizations of ideals in domain theory.
Publié le :
Classification : 18B35, 18D20, 06F07
Keywords: Quantaloid, enriched category, domain theory, fuzzy order 
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     author = {Min Liu and Shengwei Han and Isar Stubbe},
     title = {Ideals and continuity for
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     volume = {39},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a23/}
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Min Liu; Shengwei Han; Isar Stubbe. Ideals and continuity for
quantaloid-enriched categories. Theory and applications of categories, Tome 39 (2023), pp. 687-713. http://geodesic.mathdoc.fr/item/TAC_2023_39_a23/