Ideals and continuity for quantaloid-enriched categories
Category Theory
2023-04-28 v1
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.
Keywords
Cite
@article{arxiv.2304.14128,
title = {Ideals and continuity for quantaloid-enriched categories},
author = {Min Liu and Shengwei Han and Isar Stubbe},
journal= {arXiv preprint arXiv:2304.14128},
year = {2023}
}
Comments
27 pages; preprint