Detail publikačního výsledku

Localification procedure for affine systems

Solovjovs Sergejs

Originální název

Localification procedure for affine systems

Anglický název

Localification procedure for affine systems

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

Solovjovs Sergejs

Rok RIV

2017

Vydáno

01.06.2015

Místo

France

ISSN

1245-530X

Periodikum

Cahiers de Topologie et Geometrie Differentielle Categoriques

Svazek

56

Číslo

2

Stát

Francouzská republika

Strany od

109

Strany do

132

Strany počet

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"
}