Publication detail
Quasi-uniform structures and functors
IRAGI, M. HOLGATE, D.
English title
Quasi-uniform structures and functors
Type
journal article in Web of Science
Language
en
Original abstract
We study a number of categorical quasi-uniform structures induced by functors. We depart from a category C with a proper (E,M)-factorization system, then define the continuity of a C-morphism with respect to two syntopogenous structures (in particular with respect to two quasi-uniformities) on C and use it to describe the quasi-uniformities induced by pointed and copointed endofunctors of C. In particular, we demonstrate that every quasi-uniformity on a reective subcategory of C can be lifted to a coarsest quasi-uniformity on C for which every reection morphism is continuous.
English abstract
We study a number of categorical quasi-uniform structures induced by functors. We depart from a category C with a proper (E,M)-factorization system, then define the continuity of a C-morphism with respect to two syntopogenous structures (in particular with respect to two quasi-uniformities) on C and use it to describe the quasi-uniformities induced by pointed and copointed endofunctors of C. In particular, we demonstrate that every quasi-uniformity on a reective subcategory of C can be lifted to a coarsest quasi-uniformity on C for which every reection morphism is continuous.
Keywords in English
Closure operator, Syntopogenous structure, Quasi-uniform structure, (Co)pointed endofunctor, and Adjoint functor.
Released
01.10.2023
Publisher
The Mount Allison University
Location
Sackville, New Brunswick, Canada
ISSN
1201-561X
Volume
39
Number
17
Pages from–to
519–534
Pages count
16
BIBTEX
@article{BUT196767,
author="David Brendon {Holgate} and Minani {Iragi},
title="Quasi-uniform structures and functors",
year="2023",
volume="39",
number="17",
month="October",
pages="519--534",
publisher=" The Mount Allison University ",
address="Sackville, New Brunswick, Canada",
issn="1201-561X"
}