Geodesic
The category of uniform spaces as a completion of the category of metric spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 689-693

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A criterion for the existence of an initial completion of a concrete category $\bold K$ universal w.r.t\. finite products and subobjects is presented. For $\bold K=$ metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
Classification : 18A32, 18A35, 54B30, 54E15, 54E35
Keywords: universal completion; metric space; uniform space 
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     author = {Ad\'amek, Ji\v{r}{\'\i} and Reiterman, Jan},
     title = {The category of uniform spaces  as a completion of the category of metric spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Adámek, Jiří; Reiterman, Jan. The category of uniform spaces  as a completion of the category of metric spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 4, pp. 689-693. http://geodesic.mathdoc.fr/item/CMUC_1992__33_4_a13/