Publication detail

Localification procedure for affine systems

Solovjovs Sergejs

Original Title

Localification procedure for affine systems

English Title

Localification procedure for affine systems

Type

journal article - other

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.

English 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

RIV year

2015

Released

01.06.2015

Location

France

Pages from

109

Pages to

132

Pages count

23

Documents

BibTex


@article{BUT126465,
  author="Sergejs {Solovjovs}",
  title="Localification procedure for affine systems",
  annote="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.",
  chapter="126465",
  howpublished="print",
  number="2",
  volume="56",
  year="2015",
  month="june",
  pages="109--132",
  type="journal article - other"
}