Geodesic
Tight spans, Isbell completions and semi-tropical modules
Theory and applications of categories, Tome 28 (2013), pp. 696-732

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In this paper we consider generalized metric spaces in the sense of Lawvere and the categorical Isbell completion construction. We show that this is an analogue of the tight span construction of classical metric spaces, and that the Isbell completion coincides with the directed tight span of Hirai and Koichi. The notions of categorical completion and cocompletion are related to the existence of semi-tropical module structure, and it is shown that the Isbell completion (hence the directed tight span) has two different semi-tropical module structures.

Publié le :
Classification : Primary: 54E35 Secondary: 18D20, 16Y60
Keywords: Metric spaces, tropical algebra, injective hull 
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     author = {Simon Willerton},
     title = {Tight spans, {Isbell} completions and semi-tropical modules},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2013_28_a21/}
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Simon Willerton. Tight spans, Isbell completions and semi-tropical modules. Theory and applications of categories, Tome 28 (2013), pp. 696-732. http://geodesic.mathdoc.fr/item/TAC_2013_28_a21/