Publication detail

On categories of ordered sets with a closure operator

ŠLAPAL, J.

English title

On categories of ordered sets with a closure operator

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

en

Original abstract

We define and study two categories of partially ordered sets endowed with a closure operator. The first category has order-preserving and continuous maps as morphisms and it is shown to be concretely isomorphic to a category of ordered sets endowed with a compatible preorder. The second category studied has closed maps as morphisms and it is proved to be cartesian closed. As examples, consequences of these results for categories of the usual closure operators and, in particular, of topological spaces are discussed.

Keywords in English

Category, ordered set, closure operator

Released

2011-01-01

ISSN

0033-3883

Journal

PUBLICATIONES MATHEMATICAE DEBRECEN

Volume

78

Number

1

Pages from–to

61–69

Pages count

9

BIBTEX


@article{BUT49215,
  author="Josef {Šlapal}",
  title="On categories of ordered sets with a closure operator",
  journal="PUBLICATIONES MATHEMATICAE DEBRECEN",
  year="2011",
  volume="78",
  number="1",
  pages="61--69",
  issn="0033-3883"
}