Title 



Metrically generated theories


Author 





Abstract 



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 Cmetrically generated. Our main theorem proves that X is Cmetrically 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 wellknown and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.  

Language 



English


Source (journal) 



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

Publication 



Providence, R.I. : 2005


ISSN 



00029939


Volume/pages 



133:5(2005), p. 15471556


ISI 



000226466400038


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