Metrically generated theoriesMetrically generated theories
Faculty of Sciences. Mathematics and Computer Science

Fundamental Mathematics

article

2005Providence, R.I., 2005

Mathematics

Proceedings of the American Mathematical Society. - Providence, R.I., s.a.

133(2005):5, p. 1547-1556

0002-9939

000226466400038

E

English (eng)

University of Antwerp

Many examples are known of natural functors K describing the transition from categories C of generalized metric spaces to the "metrizable" objects in some given topological construct X. If K preserves initial morphisms and if K( C) is initially dense in X, then we say that X is C-metrically generated. Our main theorem proves that X is C-metrically generated if and only if X can be isomorphically described as a concretely coreflective subconstruct of a model category with objects sets structured by collections of generalized metrics in C and natural morphisms. This theorem allows for a unifying treatment of many well-known and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.

https://repository.uantwerpen.be/docman/irua/1ee30e/8141.pdf

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