Adjoint maps between implicative semilattices and continuity of localic maps

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Marcel Erné
  • Jorge Picado
  • Aleš Pultr

Externe Organisationen

  • Charles University
  • University of Coimbra
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer13
Seitenumfang23
FachzeitschriftAlgebra universalis
Jahrgang83
Ausgabenummer2
Frühes Online-Datum19 März 2022
PublikationsstatusVeröffentlicht - Mai 2022

Abstract

We study residuated homomorphisms (r-morphisms) and their adjoints, the so-called localizations (or l-morphisms), between implicative semilattices, because these objects may be characterized as semilattices whose unary meet operations have adjoints. Since left resp. right adjoint maps are the residuated resp. residual maps (having the property that preimages of principal downsets resp. upsets are again such), one may not only regard the l-morphisms as abstract continuous maps in a pointfree framework (as familiar in the complete case), but also characterize them by concrete closure-theoretical continuity properties. These concepts apply to locales (frames, complete Heyting lattices) and provide generalizations of continuous and open maps between spaces to an algebraic (not necessarily complete) pointfree setting.

ASJC Scopus Sachgebiete

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Adjoint maps between implicative semilattices and continuity of localic maps. / Erné, Marcel; Picado, Jorge; Pultr, Aleš.
in: Algebra universalis, Jahrgang 83, Nr. 2, 13, 05.2022.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Erné M, Picado J, Pultr A. Adjoint maps between implicative semilattices and continuity of localic maps. Algebra universalis. 2022 Mai;83(2):13. Epub 2022 Mär 19. doi: 10.1007/s00012-022-00767-4
Erné, Marcel ; Picado, Jorge ; Pultr, Aleš. / Adjoint maps between implicative semilattices and continuity of localic maps. in: Algebra universalis. 2022 ; Jahrgang 83, Nr. 2.
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