Detail publikace

Localification procedure for affine systems

Solovjovs Sergejs

Anglický název

Localification procedure for affine systems

Typ

článek v časopise - ostatní, Jost

Jazyk

en

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 anglicky

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

Rok RIV

2015

Vydáno

01.06.2015

Místo

France

ISSN

1245-530X

Ročník

56

Číslo

2

Strany od–do

109–132

Počet stran

23

BIBTEX


@article{BUT126465,
  author="Sergejs {Solovjovs},
  title="Localification procedure for affine systems",
  year="2015",
  volume="56",
  number="2",
  month="June",
  pages="109--132",
  address="France",
  issn="1245-530X"
}