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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
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" }