Lax algebra meets topology
type: Item
instance of: scholarly article
title: Lax algebra meets topology
zbMATH Open document ID: 1253.18006
author: Dirk Hofmann
author: Walter Tholen
published in: Topology and its Applications
publication date: 2012-06-19T00:00:00Z
review text: Let \(\mathbb{T}\) be a monad on \(Set\), which extends to the category of sets and \(V\)-valued relations for a quantale \(V\). The examples of lax algebras for this type of monad include ordered sets, metric spaces, topological spaces, closure spaces, and approach spaces for suitable choices of \(V\) and \(\mathbb{T}\). In this paper, the authors present possible candidate axiomatisations for notions of `closed map' and `proper map' in such categories of lax algebras.
reviewed by: Timothy Porter
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 18A99
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 6047969
zbMATH Keywords: monad
zbMATH Keywords: lax extension
zbMATH Keywords: lax algebra
zbMATH Keywords: compact object
zbMATH Keywords: separated object
zbMATH Keywords: perfect morphism
MaRDI profile type: Publication
full work available at URL: j.topol.2011.09.049
OpenAlex ID: W1991966037
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DOI: 10.1016/J.TOPOL.2011.09.049
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description: scientific article; zbMATH DE number 6047969