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Title: Localic maps constructed from open and closed parts
Authors: Picado, Jorge 
Pultr, Aleš 
Issue Date: 2017
Publisher: Shahid Beheshti University
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Serial title, monograph or event: Categories and General Algebraic Structures with Applications
Volume: 6
Abstract: Assembling a localic map f:L→M from localic maps f_i:S_i→M, i∈J, defined on closed resp. open sublocales (J finite in the closed case) follows the same rules as in the classical case. The corresponding classical facts immediately follow from the behavior of preimages but for obvious reasons such a proof cannot be imitated in the point-free context. Instead, we present simple proofs based on categorical reasoning. There are some related aspects of localic preimages that are of interest, though. They are investigated in the second half of the paper.
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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