Adjoint maps between implicative semilattices and continuity of localic maps

verfasst von

Marcel Erné, Jorge Picado, Aleš Pultr

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Charles University
University of Coimbra

Typ

Artikel

Journal

Algebra universalis

Band

83

Anzahl der Seiten

23

ISSN

0002-5240

Publikationsdatum

05.2022

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie, Logik

Elektronische Version(en)

https://doi.org/10.1007/s00012-022-00767-4 (Zugang: Offen)