Publication detail

Localification procedure for affine systems

Solovjovs Sergejs

Original Title

Localification procedure for affine systems

Type

journal article - other

Language

English

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

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

Authors

Solovjovs Sergejs

RIV year

2015

Released

1. 6. 2015

Location

France

ISBN

1245-530X

Periodical

Cahiers de Topologie et Geometrie Differentielle Categoriques

Year of study

56

Number

2

State

French Republic

Pages from

109

Pages to

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"
}