Publication detail

Quantale algebras as a generalization of lattice-valued frames

SOLOVJOVS, S.

English title

Quantale algebras as a generalization of lattice-valued frames

Type

journal article in Web of Science

Language

en

Original abstract

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.

English abstract

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.

Keywords in English

(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

Released

01.06.2016

Publisher

HACETTEPE UNIV, FAC SCI

Location

BEYTEPE

ISSN

1303-5010

Volume

45

Number

3

Pages from–to

781–809

Pages count

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"
}