Year: 2023
Type: article
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.
Authors: Liu, Min, Han, Shengwei, Stubbe, Isar
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367365796