Smyth complete real-enriched categories
Category Theory
2023-12-01 v1 General Topology
Abstract
This paper investigates Smyth completeness of categories enriched over a quantale obtained by equipping the unit interval of real numbers with a continuous t-norm. A real-enriched category is Smyth-complete if each of its forward Cauchy nets has a unique limit in the open ball topology of its symmetrization. It is demonstrated that Smyth completeness can be characterized as a categorical property and as a real-valued topological property. Explicitly, it is shown that a real-enriched category is Smyth complete if and only if it is separated and all of its ideals are representable, if and only if its Alexandroff real-valued topology is sober.
Cite
@article{arxiv.2311.18191,
title = {Smyth complete real-enriched categories},
author = {Junche Yu and Dexue Zhang},
journal= {arXiv preprint arXiv:2311.18191},
year = {2023}
}
Comments
26 pages