In the documentation it is said that os.path.isdir(...) an Path(...).is_dir()are equivalent substitutes.
https://docs.python.org/3/library/pathlib.html#correspondence-to-tools-in-the-os-module

But they give different result for empty path strings:
>>> import os
>>> from pathlib import Path
>>> dummy = "" 
>>> os.path.isdir(dummy)
 False

Obviously it's not an equivalence, so either this should be noted in the documentation or corrected in the code.

Forgot to write the result for Path variant:

>>> Path(dummy).is_dir()
 True

It is because Path() == Path('') == Path('.').

I understand the reasons, I only say that it does not correspond to my perception of their equivalence, because:

os.path.isdir('') != os.path.isdir('.')

while:

Path('').is_dir() == Path('.').is_dir()

and I can confirm that some libraries rely on os.path.isdir('') -> False behavior.

I think you're reading "equivalence" too strictly here to mean "exactly the same semantics". In this instance it means "for similar functionality, the equivalent method is ..." (admittedly this might be a quirk of the use of the word "equivalent" in North American English).

But I can see why you would interpret it the way you do. Please feel free to propose a PR to clarify the phrasing.

If "equivalent" is deceiving, perhaps replace it with "similary" or "roughly equivalent".  Feel free to post a PR with your preferred wording.

I am reading "equivalence" too strictly (like "as a substitute"), because this is part of the documentation :) and I agree that in ordinary speech I would use it rather in the sense of “similar”.

In order to make sure, that everyone agrees only on that this requires only a documentation change? Because as for me, I think that it will better for `os.path.isdir` to raise `ValueError` or `DeprecationWarning` - `False` on empty string is not well defined behavior. But I'm fine to be alone with the last one.

Changing the semantics of os.path.isdir() for something like this isn't worth breaking code; basically it's now a quirk of the function.