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Topological categories. (English) Zbl 0551.18003
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).
Reviewer: H.Herrlich

MSC:
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18-02 Research exposition (monographs, survey articles) pertaining to category theory
54B30 Categorical methods in general topology
54-02 Research exposition (monographs, survey articles) pertaining to general topology
18A22 Special properties of functors (faithful, full, etc.)
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References:
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