Publication result detail

Topogenous orders and related families of morphisms

HOLGATE, D.; IRAGI, M.

Original Title

Topogenous orders and related families of morphisms

English Title

Topogenous orders and related families of morphisms

Type

WoS Article

Original Abstract

In a category with a proper ()-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow simultaneous study of four classes of morphisms obtained separately with respect to closure, interior and neighbourhood operators, the initial and final morphisms lead us to the study of topogenous orders induced by pointed and co-pointed endofunctors. We also lift the topogenous orders along an -fibration. This permits one to obtain the lifting of interior and neighbourhood operators along an -fibration and includes the lifting of closure operators found in the literature. A number of examples presented at the end of the paper demonstrates our results.

English abstract

In a category with a proper ()-factorization system, we study the notions of strict, co-strict, initial and final morphisms with respect to a topogenous order. Besides showing that they allow simultaneous study of four classes of morphisms obtained separately with respect to closure, interior and neighbourhood operators, the initial and final morphisms lead us to the study of topogenous orders induced by pointed and co-pointed endofunctors. We also lift the topogenous orders along an -fibration. This permits one to obtain the lifting of interior and neighbourhood operators along an -fibration and includes the lifting of closure operators found in the literature. A number of examples presented at the end of the paper demonstrates our results.

Keywords

18A05; 18F60; 54A15; 54B30; Closure operator; interior operator; categorical topogenous order; heredity; (co)pointed endofunctors; -fibrations; strict; co-strict; initial and final morphisms

Key words in English

18A05; 18F60; 54A15; 54B30; Closure operator; interior operator; categorical topogenous order; heredity; (co)pointed endofunctors; -fibrations; strict; co-strict; initial and final morphisms

Authors

HOLGATE, D.; IRAGI, M.

RIV year

2024

Released

01.11.2023

Publisher

TAYLOR & FRANCIS LTD

Location

ABINGDON

ISBN

1607-3606

Periodical

Quaestiones Mathematicae

Volume

46

Number

S1

State

Republic of South Africa

Pages from

223

Pages to

238

Pages count

16

URL

https://www.researchgate.net/publication/369627134_Topogeneous_orders_and_related_families_of_morphisms

BibTex

@article{BUT187314,
  author="David {Holgate} and Minani {Iragi}",
  title="Topogenous orders and related families of morphisms",
  journal="Quaestiones Mathematicae",
  year="2023",
  volume="46",
  number="S1",
  pages="223--238",
  doi="10.2989/16073606.2023.2247739",
  issn="1607-3606",
  url="https://www.researchgate.net/publication/369627134_Topogeneous_orders_and_related_families_of_morphisms"
}