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 it sends closed sets into compact setsthe 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.

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 it sends closed sets into compact sets, $A\Subset B$

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.