English

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

R2 v1 2026-06-28T10:19:36.206Z