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Ideals and continuity for
quantaloid-enriched categories

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Min Liu, Shengwei Han and Isar Stubbe

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.

Keywords:
Quantaloid, enriched category, domain theory, fuzzy order

2020 MSC:
18B35, 18D20, 06F07

*Theory and Applications of Categories,*
Vol. 39, 2023,
No. 24, pp 687-713.

Published 2023-08-17.

http://www.tac.mta.ca/tac/volumes/39/24/39-24.pdf

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