Left adjoint for Booleanization
type: Item
instance of: scholarly article
title: Left adjoint for Booleanization
zbMATH Open document ID: 0915.06006
DOI: 10.1023/A:1008669807789
author: Josef Niederle
published in: Applied Categorical Structures
publication date: 1999-07-05T00:00:00Z
review text: A frame is a complete distributive lattice \(L\) in which \(a\wedge\bigvee_{b\in B}b=\bigvee_{b\in B}(a\wedge b)\) for each \(a\in L\) and \(B\subseteq L\). Boolean frames are precisely complete Boolean lattices. If \(L\) is a frame then the set \({\mathcal B}(L)=\{a\in L/a=a^{**}\}\) (where \(a^*\) is the pseudocomplement of a) of all skeletal elements in \(L\) forms a Boolean frame with respect to the induced order, which is called the Booleanization of \(L\). The scope of this paper is to construct many left adjoints for Booleanization in suitable categories.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 06D15
zbMATH DE Number: 1234347
zbMATH Keywords: categories of frames
zbMATH Keywords: Boolean frames
zbMATH Keywords: pseudocomplement
zbMATH Keywords: Booleanization
zbMATH Keywords: left adjoints
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: a:1008669807789
OpenAlex ID: W48693018
description: scientific article; zbMATH DE number 1234347