Detail publikace

Quantale algebras as a generalization of lattice-valued frames

SOLOVJOVS, S.

Anglický název

Quantale algebras as a generalization of lattice-valued frames

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

en

Originální abstrakt

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued frame, which are currently available in the literature. Moreover, we obtain a convenient setting for lattice-valued extensions of the famous equivalence between the categories of sober topological spaces and spatial locales, as well as for answering the question on its relationships to the notion of stratification of lattice-valued topological spaces.

Anglický abstrakt

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued frame, which are currently available in the literature. Moreover, we obtain a convenient setting for lattice-valued extensions of the famous equivalence between the categories of sober topological spaces and spatial locales, as well as for answering the question on its relationships to the notion of stratification of lattice-valued topological spaces.

Klíčová slova anglicky

(Cocomplete) (skeletal) Q-category; lattice-valued frame; lattice-valued partially ordered set; quantale; quantale algebra; quantale module; sober topological space; spatial locale; stratification degree; stratified topological space

Vydáno

01.06.2016

Nakladatel

HACETTEPE UNIV, FAC SCI

Místo

BEYTEPE

ISSN

1303-5010

Ročník

45

Číslo

3

Strany od–do

781–809

Počet stran

29

BIBTEX


@article{BUT171013,
  author="Sergejs {Solovjovs},
  title="Quantale algebras as a generalization of lattice-valued frames",
  year="2016",
  volume="45",
  number="3",
  month="June",
  pages="781--809",
  publisher="HACETTEPE UNIV, FAC SCI",
  address="BEYTEPE",
  issn="1303-5010"
}