is an isometric embedding. Thus it follows that every space aimed at X can be isometrically mapped into Aim(X), with some additional (essential) categorical requirements satisfied. The space Aim(X) is injective (hyperconvex in the sense of Aronszajn-Panitchpakdi) – given a metric space M, which contains Aim(X) as a metric subspace, there is a canonical (and explicit) metric retraction of M onto Aim(X) . References Metric geometry