Notation for "the inclusion map is a homotopy equivalence"

$Astackrel{sim}{hookrightarrow}B$? Alternatively, using Oberdiek's stackrel.sty you could say something like

A mathrel{raisebox{2pt}{$stackrel[raisebox{1pt}{$sim$}]{}subset$}} B

and play a little with the raiseboxes so that this aligns more or less correctly (this depends on your final font, and your publisher's typographer is not going to love you for this...)