Kategoriální přístup ke konvergenci

A categorical approach to convergence

článek v časopise ve Web of Science, Jimp

en

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.

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.

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.

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

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

15.12.2016

University of Niś

Niś, Serbia

0354-5180

30

12

3329–3338

10