CI: start testing Python 3.11
- [ ] xref #46680 (Replace xxxx with the Github issue number)
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Is this going to supersede https://github.com/pandas-dev/pandas/pull/47032?  > 

Didn't realize there is an existing PR... You can just push to my PR directly if you want, or pull the changes here. It's a little farther down the pipeline, but I will not have time to work on it in the near future. ```
FAILED pandas/tests/arrays/categorical/test_api.py::TestCategoricalAPI::test_set_ordered
FAILED pandas/tests/arrays/categorical/test_api.py::TestPrivateCategoricalAPI::test_codes_immutable
FAILED pandas/tests/indexes/multi/test_get_set.py::test_set_levels_codes_directly
FAILED pandas/tests/indexes/period/test_freq_attr.py::TestFreq::test_freq_setter_deprecated
FAILED pandas/tests/io/parser/test_quoting.py::test_null_quote_char[python--0]
FAILED pandas/tests/io/parser/test_quoting.py::test_null_quote_char[python--3]
FAILED pandas/tests/io/parser/common/test_read_errors.py::test_null_byte_char[python]
ERROR pandas/tests/scalar/test_nat.py - TypeError: '<' not supported between ...
ERROR pandas/tests/scalar/test_nat.py - TypeError: '<' not supported between ...
``` FYI Windows will also fail until #47467 is merged in. Hello @fangchenli! Thanks for updating this PR. We checked the lines you've touched for [PEP 8](https://www.python.org/dev/peps/pep-0008) issues, and found:















There are currently no PEP 8 issues detected in this Pull Request. Cheers! :beers: 

##### Comment last updated at 2022-08-17 19:19:05 UTC @fangchenli 
Thanks for picking this up. There haven't been commits on this PR in a while, so I was wondering whether you had the time to finish this PR up.

I've merged main into this PR for you just to see where we're at with the failures.

I'm pretty close to finishing off #47467, and am going to try to get it merged this week. I think I have enough time where I'll be able to finish it up, hopefully before 3.11rc1. I accidentally pushed some commits here(I misconfigured github cli-meant to push to my own branch and pull request to this one), so I decided to go all the way to getting CI green. Sorry about the noise.

At any rate, this is ready now pending #47467 merge.  @lithomas1 Thank you very much for finishing this up. > @lithomas1 Thank you very much for finishing this up.

Thanks for picking this up again.