Detail výsledku – FaVU VUT

Originální název

Topogenous orders and related families of morphisms

Anglický název

Topogenous orders and related families of morphisms

Druh

Článek WoS

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

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

Klíčová slova v angličtině

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

Autoři

HOLGATE, D.; IRAGI, M.

Rok RIV

2024

Vydáno

01.11.2023

Nakladatel

TAYLOR & FRANCIS LTD

Místo

ABINGDON

ISSN

1607-3606

Periodikum

Quaestiones Mathematicae

Svazek

46

Číslo

S1

Stát

Jihoafrická republika

Strany od

223

Strany do

238

Strany počet

16

URL

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

Plný text v Digitální knihovně

http://hdl.handle.net/

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"
}