Publication result detail

Transitive quasi-uniform structures depending on a parameter

IRAGI, M., ŠLAPAL, J.

Original Title

Transitive quasi-uniform structures depending on a parameter

English Title

Transitive quasi-uniform structures depending on a parameter

Type

WoS Article

Original Abstract

In a category C with an (E,M)-factorization structure for morphisms, we prove that any subclass N of M which is closed under pullbacks determines a transitive quasi-uniform structure on C. In addition to providing a categorical characterization of all transitive quasiuniform structures compatible with a topology, this result also permits us to establish a number of Galois connections related to quasi-uniform structures on C. These Galois connections lead to the description of subcategories of C determined by quasi-uniform structures. Several examples considered at the end of the paper illustrate our results.

English abstract

In a category C with an (E,M)-factorization structure for morphisms, we prove that any subclass N of M which is closed under pullbacks determines a transitive quasi-uniform structure on C. In addition to providing a categorical characterization of all transitive quasiuniform structures compatible with a topology, this result also permits us to establish a number of Galois connections related to quasi-uniform structures on C. These Galois connections lead to the description of subcategories of C determined by quasi-uniform structures. Several examples considered at the end of the paper illustrate our results.

Keywords

Closure operator, Quasi-uniform structure, Syntopogenous structure, Galois connection, Interior operator.

Key words in English

Closure operator, Quasi-uniform structure, Syntopogenous structure, Galois connection, Interior operator.

Authors

IRAGI, M., ŠLAPAL, J.

RIV year

2024

Released

10.08.2023

Publisher

Springer

Location

Basel

ISBN

0001-9054

Periodical

Aequationes Mathematicae

Volume

97

Number

4

State

Swiss Confederation

Pages from

823

Pages to

836

Pages count

14

URL

https://link.springer.com/article/10.1007/s00010-022-00937-8

BibTex

@article{BUT183729,
  author="Josef {Šlapal} and Minani {Iragi}",
  title="Transitive quasi-uniform structures depending on a parameter",
  journal="Aequationes Mathematicae",
  year="2023",
  volume="97",
  number="4",
  pages="823--836",
  doi="10.1007/s00010-022-00937-8",
  issn="0001-9054",
  url="https://link.springer.com/article/10.1007/s00010-022-00937-8"
}