Publication detail

Topogenous orders on forms

IRAGI, M. HOLGATE, D. ŠLAPAL, J.

English title

Topogenous orders on forms

Type

journal article in Web of Science

Language

en

Original abstract

Departing from a categorical concept of topogenous orders defined relative to the bifibration of subobjects, we introduce and discuss topogenous orders on forms, i.e., faithful and amnestic functors. These topogenous orders are shown to include both closure and interior operators on forms. We define and study two special morphisms relative to a topogenous order, namely strict and final morhisms. We give a characterization of the two morphisms by the help of their cartesian and cocartesian liftings. Some examples from topology and algebra demonstrating our results are included.

English abstract

Departing from a categorical concept of topogenous orders defined relative to the bifibration of subobjects, we introduce and discuss topogenous orders on forms, i.e., faithful and amnestic functors. These topogenous orders are shown to include both closure and interior operators on forms. We define and study two special morphisms relative to a topogenous order, namely strict and final morhisms. We give a characterization of the two morphisms by the help of their cartesian and cocartesian liftings. Some examples from topology and algebra demonstrating our results are included.

Keywords in English

Form, (co)cartesian lifting, closure operator, interior operator, topogenous order, strict and nal morphisms, cohereditariness.

Released

01.02.2025

Publisher

De Gruyter

Location

Slovakia

ISSN

0139-9918

Volume

75

Number

1

Pages from–to

179–188

Pages count

10

BIBTEX


@article{BUT197833,
  author="Josef {Šlapal} and Minani {Iragi} and David Brendon {Holgate},
  title="Topogenous orders on forms",
  year="2025",
  volume="75",
  number="1",
  month="February",
  pages="179--188",
  publisher="De Gruyter",
  address="Slovakia",
  issn="0139-9918"
}