Editing Metric map (section)

==Category of metric maps==
The [[function composition]] of two metric maps is another metric map, and the [[identity map]] <math>\mathrm{id}_M\colon M \rightarrow M</math> on a metric space <math>M</math> is a metric map, which is also the [[identity element]] for function composition. Thus metric spaces together with metric maps form a [[Category (mathematics)|category]] '''[[Category of metric spaces|Met]]'''. '''Met''' is a [[subcategory]] of the category of metric spaces and Lipschitz functions. A map  between metric spaces is an [[isometry]] if and only if it is a [[bijective]] metric map whose [[Inverse function|inverse]] is also a metric map. Thus the [[isomorphism]]s in '''Met''' are precisely the isometries.