# Notation for “the inclusion map is a homotopy equivalence”

It's sometimes convenient to have different notations for "$A$ is a subset of $B$" depending on what the inclusion map does:

1. If it's non-surjective, $A\subsetneq B$ or $A\subset B$, depending on your religion
2. If it's surjective, $A=B$ :)
3. If the image is a precompact set, $A\Subset B$

Does there exist notation to indicate that the inclusion $A\hookrightarrow B$ is a homotopy equivalence? I'd like to use something similar to 1-3.

-

$A\stackrel{\sim}{\hookrightarrow}B$? Alternatively, using Oberdiek's stackrel.sty you could say something like
A \mathrel{\raisebox{2pt}{$\stackrel[\raisebox{1pt}{$\sim$}]{}\subset$}} B