Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Yu, Junche, Zhang, Dexue
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4389260840