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Oh, wait. why are you making the PR to the 3.6 branch? It looks like this also needs to be added to 3.7 and master. Could you please close this one and re-open w.r.t. master branch? I will then merge and backport to other relevant branches (this is how things are normally done here).

Okay, I'll mention you in the new pull request.

Actually, 3.7+ has contextlib.AbstractAsyncContextManager but 3.6 has no such equivalent. Should the documentation for 3.6 and 3.7 be different? The rest of the documentation tends to be along the lines of

   A generic version of ...

so for 3.7 we could say

A generic version of :class:`contextlib.AbstractAsyncContextManager`.

but not for 3.6.

In fact, seems 3.6 has some weird dodging around the absence of contextlib.AbstractAsyncContextManager.

It is OK to have different text for different versions. You can make two PRs, one against master with Generic version of ..., and one against 3.6 with something like An abstract class with __aenter__ and __aexit__ methods (you can just copy this from current docs in collections.abc).