Publication result detail
Quasi-uniform structures and functors
IRAGI, M.; HOLGATE, D.
Original Title
Quasi-uniform structures and functors
English Title
Quasi-uniform structures and functors
Type
WoS Article
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
Closure operator, Syntopogenous structure, Quasi-uniform structure, (Co)pointed endofunctor, and Adjoint functor.
Key words in English
Closure operator, Syntopogenous structure, Quasi-uniform structure, (Co)pointed endofunctor, and Adjoint functor.
Authors
IRAGI, M.; HOLGATE, D.
RIV year
2025
Released
01.10.2023
Publisher
The Mount Allison University
Location
Sackville, New Brunswick, Canada
ISBN
1201-561X
Periodical
Theory and Applications of Categories
Volume
39
Number
17
State
Canada
Pages from
519
Pages to
534
Pages count
16
URL
BibTex
@article{BUT196767,
author="David Brendon {Holgate} and Minani {Iragi}",
title="Quasi-uniform structures and functors",
journal="Theory and Applications of Categories",
year="2023",
volume="39",
number="17",
pages="519--534",
issn="1201-561X",
url="http://www.tac.mta.ca/tac/volumes/39/17/39-17.pdf"
}