most recent 30 from http://mathoverflow.net 2013-05-25T11:22:59Z http://mathoverflow.net/feeds/question/79817 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/79817/reference-requestenriched-categories-metric-on-lipschitz-continuous-functions Garlef Wegart 2011-11-02T11:11:36Z 2011-11-02T12:13:06Z

<p>If we consider metric spaces to be categories enriched over $\mathbb R_{\geq 0}$, the object corresponding to presheaves should be lipschitz-continuous functions $\operatorname{Lip^ 1}(M, \mathbb R_{\geq 0})$. Now there should be an obvious metric on this set; making the Yoneda map $$x\mapsto \operatorname d(-,x)$$ an isometric embedding. <strong>What is this metric?</strong></p>

http://mathoverflow.net/questions/79817/reference-requestenriched-categories-metric-on-lipschitz-continuous-functions/79823#79823 Finn Lawler 2011-11-02T12:13:06Z 2011-11-02T12:13:06Z

<p>It is the usual sup metric. See section 2 of Lawvere's original <a href="http://www.tac.mta.ca/tac/reprints/articles/1/tr1abs.html" rel="nofollow">article</a>.</p>