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Title
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Metrically generated theories
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Proceedings of the American Mathematical Society. - Providence, R.I., s.a.
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Publication
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Providence, R.I.
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2005
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ISSN
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0002-9939
[print]
1088-6826
[online]
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DOI
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10.1090/S0002-9939-04-07633-6
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Volume/pages
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133
:5
(2005)
, p. 1547-1556
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ISI
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000226466400038
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Full text (Publisher's DOI)
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Full text (open access)
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