Topological categories
type: Item
instance of: scholarly article
title: Topological categories
zbMATH Open document ID: 0551.18003
DOI: 10.1016/0166-8641(84)90029-4
author: G. C. L. Brümmer
published in: Topology and its Applications
publication date: 1984-01-01T00:00:00Z
review text: The investigation of topological resp. initially complete categories is a central topic of categorical topology. The article under review, a survey of the theory of initially complete categories, is a well written, highly stimulating supplement to the reviewers survey article 'Categorical topology 1971-1981' [ Proc. 5th Prague Topol. Symp. 1981, Sigma Ser. Pure Math. 3, 279-383 (1983; Zbl 0502.54001)]. Besides its survey character, the paper contains several new inspiring developments. In particular, the author discusses the concept of ''structural layers'' and demonstrates that for topological settings the two perceptions of, on one hand, increasing richness in structure and, on the other hand, increasing generality, are only the result of the viewpoints taken and are in fact one and the same thing. This circumstance is in fact one of the surprising distinctions between topology and algebra. Moreover it accounts for the fact that it is possible to accomodate various structural levels of general topology into a single setting (e.g. merotopic spaces, nearness space, syntopogenous space).
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 18-02
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54-02
Mathematics Subject Classification ID: 18A22
zbMATH DE Number: 3877386
zbMATH Keywords: topological category
zbMATH Keywords: concrete category
zbMATH Keywords: topologically-algebraic functor
zbMATH Keywords: semi-topological functor
zbMATH Keywords: initially complete categories
zbMATH Keywords: categorical topology
zbMATH Keywords: survey
zbMATH Keywords: structural layers
MaRDI profile type: Publication
full work available at URL: 0166-8641(84)90029-4
OpenAlex ID: W4213346735
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