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arXiv · 2304.14128

Ideals and continuity for quantaloid-enriched categories

Min Liu·Shengwei Han·Isar Stubbe
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Abstract

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 Phi of presheaves, we define and study the Phi-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.

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Min Liu, Shengwei Han, Isar Stubbe. 2023-04-27. Ideals and continuity for quantaloid-enriched categories. https://arxiv.org/abs/2304.14128

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