Publication detail

Transitive quasi-uniform structures depending on a parameter

IRAGI, M. ŠLAPAL, J.

English title

Transitive quasi-uniform structures depending on a parameter

Type

journal article in Web of Science

Language

en

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 in English

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

Released

10.08.2023

Publisher

Springer

Location

Basel

ISSN

0001-9054

Volume

97

Number

4

Pages from–to

823–836

Pages count

14

BIBTEX


@article{BUT183729,
  author="Josef {Šlapal} and Minani {Iragi},
  title="Transitive quasi-uniform structures depending on a parameter",
  year="2023",
  volume="97",
  number="4",
  month="August",
  pages="823--836",
  publisher="Springer",
  address="Basel",
  issn="0001-9054"
}