Detail publikace

Topogenous orders and related families of morphisms

HOLGATE, D. IRAGI, M.

Anglický název

Topogenous orders and related families of morphisms

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova anglicky

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

Vydáno

01.11.2023

Nakladatel

TAYLOR & FRANCIS LTD

Místo

ABINGDON

ISSN

1607-3606

Ročník

46

Číslo

S1

Strany od–do

223–238

Počet stran

16

BIBTEX


@article{BUT187314,
  author="David {Holgate} and Minani {Iragi},
  title="Topogenous orders and related families of morphisms",
  year="2023",
  volume="46",
  number="S1",
  month="November",
  pages="223--238",
  publisher="TAYLOR & FRANCIS LTD",
  address="ABINGDON",
  issn="1607-3606"
}