Publication detail

A categorical approach to convergence

ŠLAPAL, J.

Czech title

Kategoriální přístup ke konvergenci

English title

A categorical approach to convergence

Type

journal article in Web of Science

Language

en

Original abstract

We define the concept of a convergence classes on an object of a given category by using certain generalized nets for expressing the convergence. The resulting topological category, whose objects are the pairs consisting of objects of the original category and convergence classes on them, is then investigated. We study full subcategories of this category which are obtained by imposing some natural convergence axioms. In particular, we find sufficient conditions for the subcategories to be cartesian closed. We also investigate behavior of the closure operators associated with the convergence in a natural way.

Czech abstract

V práci je definován koncept konvergenční třídy na objektu dané kategorie pomocí jistých zobecněných sítí. Výslední topologické kategorie, jejímiž objekty jsou dvojice tvořené objekty původní kastegorie a konvergenčními třídami ma nich je studována. Zejména jsou vyšetřévány úplná padkategorie této kategorie dané přirozenými konvergenčními axiomy. Mimo jiné jsou nalezeny podmínky, za pterých jsou tyto podkategorie kartézsky uzavřené. convergence classes on them, is then investigated. We study full subcategories of this category which are obtained by imposing some natural convergence axioms. In particular, we find sufficient conditions for the subcategories to be cartesian closed. We also investigate behavior of the closure operators associated with the convergence in a natural way.

English abstract

We define the concept of a convergence classes on an object of a given category by using certain generalized nets for expressing the convergence. The resulting topological category, whose objects are the pairs consisting of objects of the original category and convergence classes on them, is then investigated. We study full subcategories of this category which are obtained by imposing some natural convergence axioms. In particular, we find sufficient conditions for the subcategories to be cartesian closed. We also investigate behavior of the closure operators associated with the convergence in a natural way.

Keywords in Czech

Gobecněná síť a podsíť, konvergence, topologická kategorie, kartézsky uzavřená kategorie, kategoriální uzávěrový operátor.

Keywords in English

Generalized net and subnet, convergence, topological category, cartesian closed category, categorical closure operator

Released

15.12.2016

Publisher

University of Niś

Location

Niś, Serbia

ISSN

0354-5180

Volume

30

Number

12

Pages from–to

3329–3338

Pages count

10

BIBTEX


@article{BUT113319,
  author="Josef {Šlapal},
  title="A categorical approach to convergence",
  year="2016",
  volume="30",
  number="12",
  month="December",
  pages="3329--3338",
  publisher="University of Niś",
  address="Niś, Serbia",
  issn="0354-5180"
}