API: register_extension_dtype class decorator
Closes https://github.com/pandas-dev/pandas/issues/22664
Hello @TomAugspurger! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/api/extensions/__init__.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/api/extensions/__init__.py) !

 - There are no PEP8 issues in the file [`pandas/core/dtypes/dtypes.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/core/dtypes/dtypes.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/base/dtype.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/tests/extension/base/dtype.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/decimal/test_decimal.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/tests/extension/decimal/test_decimal.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/json/test_json.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/tests/extension/json/test_json.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/test_categorical.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/tests/extension/test_categorical.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/test_integer.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/tests/extension/test_integer.py) !

 - There are no PEP8 issues in the file [`pandas/tests/extension/test_interval.py`](https://github.com/TomAugspurger/pandas/blob/98ac0471080f397f163eb809fefc8909e02db1cb/pandas/tests/extension/test_interval.py) !

 also can you change the registration of the pandas EA types to use the new register function (e.g. Categorical, Interval etc) # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=h1) Report
> Merging [#22666](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/73dd6ece3b66008eb8077098c101d0e300b1e714?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/22666/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #22666      +/-   ##
==========================================
+ Coverage   92.17%   92.17%   +<.01%     
==========================================
  Files         169      169              
  Lines       50708    50717       +9     
==========================================
+ Hits        46740    46749       +9     
  Misses       3968     3968
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.58% <100%> (ø)` | :arrow_up: |
| #single | `42.36% <100%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/dtypes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2Jhc2UucHk=) | `100% <ø> (ø)` | :arrow_up: |
| [pandas/core/dtypes/dtypes.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2R0eXBlcy5weQ==) | `96.08% <100%> (+0.03%)` | :arrow_up: |
| [pandas/core/arrays/integer.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2ludGVnZXIucHk=) | `94.53% <100%> (-0.03%)` | :arrow_down: |
| [pandas/api/extensions/\_\_init\_\_.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2FwaS9leHRlbnNpb25zL19faW5pdF9fLnB5) | `100% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.45% <0%> (ø)` | :arrow_up: |
| [pandas/core/indexes/multi.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9tdWx0aS5weQ==) | `95.41% <0%> (ø)` | :arrow_up: |
| [pandas/io/formats/style.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvc3R5bGUucHk=) | `96.43% <0%> (ø)` | :arrow_up: |
| [pandas/core/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/22666/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY29tbW9uLnB5) | `97.39% <0%> (+0.05%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=footer). Last update [73dd6ec...2a21f7c](https://codecov.io/gh/pandas-dev/pandas/pull/22666?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 Updated for categorical and interval. Couldn't do the same for the various Integer dtypes, since they're generated dynamically. > Couldn't do the same for the various Integer dtypes, since they're generated dynamically.

https://github.com/pandas-dev/pandas/blob/master/pandas/core/arrays/integer.py#L621

just a 1-liner to change Right... fixed. All green (this was split from the SparseArray PR fyi. I think I have one or two more things to split before) lgtm

though i think should re-evaluate the test (could be that wasn’t testing anything), but this should have a test