Publication detail

Localification procedure for affine systems

Solovjovs Sergejs

English title

Localification procedure for affine systems

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

en

Original abstract

Motivated by the concept of affine set of Y. Diers, this paper studies the notion of affine system, extending topological systems of S. Vickers. The category of affine sets is isomorphic to a full coreflective subcategory of the category of affine systems. We show the necessary and sufficient condition for the dual category of the variety of algebras, underlying affine sets, to be isomorphic to a full reflective subcategory of the category of affine systems. As a consequence, we arrive at a restatement of the sobriety-spatiality equivalence for affine sets, patterned after the equivalence between the categories of sober topological spaces and spatial locales.

Keywords in English

Adjoint situation, affine set, (co)reflective subcategory, sober topological space, spatial locale, state property system, T0 topological space, topological system, variety

Released

2015-06-01

Location

France

ISSN

1245-530X

Journal

Cahiers de Topologie et Geometrie Differentielle Categoriques

Volume

56

Number

2

Pages from–to

109–132

Pages count

23

BIBTEX


@article{BUT126465,
  author="Sergejs {Solovjovs}",
  title="Localification procedure for affine systems",
  journal="Cahiers de Topologie et Geometrie Differentielle Categoriques",
  year="2015",
  volume="56",
  number="2",
  pages="109--132",
  issn="1245-530X"
}