Met-like categories amongst concrete topological categories
type: Item
instance of: scholarly article
title: Met-like categories amongst concrete topological categories
zbMATH Open document ID: 1407.18004
author: Walter Tholen
published in: Applied Categorical Structures
publication date: 2018-10-15T00:00:00Z
review text: For any quantale \(\mathsf{V}\), \(\mathsf{V}\)-\(\mathbf{Cat}\) is well known to be a concrete topological category which symmetric monoidal closed. The principal objective in this paper is to consider how to recognize full bireflective subcategories of such quantale-induced topological categories amongst all concrete topological categories, which is to be accounted the first step in an incandescent program aiming to characterize the quantale-monad-enriched categories \((\mathbb{T},\mathsf{V})\)-\(\mathbf{Cat}\), as can be seen in [\textit{M. M. Clementino} and \textit{D. Hofmann}, Appl. Categ. Struct. 11, No. 3, 267--286 (2003; Zbl 1024.18003)], [\textit{M. M. Clementino} et al., Appl. Categ. Struct. 12, No. 2, 127--154 (2004; Zbl 1051.18005)], [\textit{M. M. Clementino} and \textit{W. Tholen}, J. Pure Appl. Algebra 179, No. 1--2, 13--47 (2003; Zbl 1015.18004)], [\textit{D. Hofmann}, Adv. Math. 215, No. 2, 789--824 (2007; Zbl 1127.18001)], [\textit{D. Hofmann} (ed.) et al., Monoidal topology. A categorical approach to order, metric, and topology. Cambridge: Cambridge University Press (2014; Zbl 1297.18001)], [\textit{G. J. Seal}, Theory Appl. Categ. 14, 221--243 (2005; Zbl 1088.18006)], [\textit{H. Lai} et al., Theory Appl. Categ. 32, 736--768 (2017; Zbl 1374.18011)], [\textit{W. Tholen}, ``Lax distributive laws for topology. I'', \url{arXiv:1603.06251}], [\textit{R. Lowen}, Approach spaces: the missing link in the topology-uniformity-metric triad. Oxford: Clarendon Press (1997; Zbl 0891.54001)], [\textit{R. Lowen}, Index analysis. Approach theory at work. London: Springer (2015; Zbl 1311.54002)].
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18D30
zbMATH DE Number: 6954317
zbMATH Keywords: topological category
zbMATH Keywords: symmetric monoidal closed category
zbMATH Keywords: quantale-enriched category
zbMATH Keywords: prequantalic topological category
zbMATH Keywords: transitive topological category
zbMATH Keywords: symmetric topological category
MaRDI profile type: Publication
full work available at URL: s10485-018-9513-7
OpenAlex ID: W2791873208
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DOI: 10.1007/S10485-018-9513-7
description: scientific article; zbMATH DE number 6954317