FIX: REGR: setting numeric value in Categorical Series with enlargement raise internal error
- [x] closes #47677
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- [x] Added an entry in the latest `doc/source/whatsnew/v1.5.0.rst` file if fixing a bug or adding a new feature.

> What happens when a string is used for enlarging? Like a

The series is also cast to `object`, which might not be the behaviour we want. But this also happens previous to the regression (tested on `v1.4.3`). Yeah this is also a bug then. Could you check if the categorical dtypes match and then return the dtype accordingly? > Yeah this is also a bug then. Could you check if the categorical dtypes match and then return the dtype accordingly?

How should we tackle that problem? If the enlarging value can be cast to categorical we should end up with a categorical series (so enlarging with `0` as in the issue also yields a categorical series)? Or only if the enlarging value is already one of the categories?
 How does concat behave in that case? > How does concat behave in that case?

Like this 
```python
import pandas as pd
s = pd.Series(["a", "b", "c"], dtype="category")
t = pd.concat([s, pd.Series(["a"], index=[3])])  # dtype: object
t2 = pd.concat([s, pd.Series(["a"], index=[3], dtype="category")])  # dtype: object
```
I would consider this fine for `t` but not for `t2`. Note that I checked this for v1.4.3 and my fix and the behaviour is the same for both. Yeah I think t2 is off  Could you try t2 with categories specified as a,b, c? > Could you try t2 with categories specified as a,b, c?

This is interesting:
```python
t = pd.concat([s, pd.Series(["a"])]) # dtype object
t2 = pd.concat([s, pd.Series(["a"], dtype="category")])  # dtype object
t3 = pd.concat([s, pd.Series(["a", "b"], dtype="category")]) # dtype object
t4 = pd.concat([s, pd.Series(["a", "b", "c"], dtype="category")])  # dtype category
t5 = pd.concat([s, pd.Series(["a", "b", "a", "b", "c"], dtype="category")]) #dtype category
t6 = pd.concat([s, pd.Series(["a", "b", "a", "b", "a"], dtype="category")]) #dtype object
t7 = pd.concat([s, pd.Series(["a", "b", "d"], dtype="category")])  # dtype object
```
Only if the categories are match exactly we preserve the category type. This looks really buggy. But this is not a regression, checked it on v1.4.3, main and my fix and the behaviour is identical on all. Should we create a seperate issue for this? No this make sense, the dtypes are not equal with different categories. But enlargement with a scalar is a different case, we should preserve categorical dtype there. We have to create a series with the correct categories in that case  > No this make sense, the dtypes are not equal with different categories. But enlargement with a scalar is a different case, we should preserve categorical dtype there. We have to create a series with the correct categories in that case

I updated the PR to preserve the categorical dtype if the enlarging element is already in the categories. I needed a special case
in `_setitem_with_indexer_missing` for this since we don't want to change `concat_compat` for this.

Please note that in
```python
s = pd.DataFrame([["a", "b"], ["c", "k"]], dtype="category")
s.loc[3] = "a"
```
both axis are cast to `object`. This behaviour was not changed. But to be consistent I would expect, that the first column should stay categorical while the second should change. DataFrame cases don't work yet, this is correct. But this has multiple issues still, so lets focus on Series here Could you also add a test where we enlarge with nan? This is not part of the categories but should probably work? Not sure  > Could you also add a test where we enlarge with nan? This is not part of the categories but should probably work? Not sure

Yep, it works in the sense that after enlarging with nan the series has dtype object. But I think that's fine. I added the test I was referring to the opposite.

```
result = Series([1, 2, 3], dtype=pd.CategoricalDtype(categories=pd.Index([1, 2, 3])))
result.loc[1] = np.nan  # np.nan and pd.NA
```

this keeps categorical dtype, e.g. enlargement should too. Could you add tests for enlarging and setting into it to test that they are consistent?

Could you also add tests so that the integer dtype is kept like above? e.g. Int64 stays Int64, Int32 stays Int32 and so on. (we have fixtures for that) > you also add tests so that the integer dtype is kept like above? e.g. Int64 stays Int64, Int32 stays Int32 and so on. (we have fixtures for that)

Found one fixture in `tests/groupby/test_function.py` called `dtypes_for_minmax` but that doesn't look for reusing in other files. Also didn't check for `np.int32` and `np.float32` since 
```python 
pd.CategoricalDtype(pd.array([1, 2, 3], dtype=np.int32)).__dict__
>>> {'_categories': Int64Index([1, 2, 3], dtype='int64'), '_ordered': False}
```
these are cast implicitly. Its called something like any_numeric_dtype > Its called something like any_numeric_dtype

used `any_numeric_ea_dtype` for this, seems like the most generic fixture available for this case I think there exists one that includes numpy dtypes, but this would work too  > I think there exists one that includes numpy dtypes, but this would work too

besides that I still don't find a unified extension array + numpy dtype fixture it seems like this wouldn't work for `np.int32` and `np.float32` since these are implicitly cast to their `64` bit counterparts
```python
pd.CategoricalDtype(np.array([1, 2, 3], dtype=np.int32)).__dict__
>>> {'_categories': Int64Index([1, 2, 3], dtype='int64'), '_ordered': False}
``` Could you try Index([1, 2, 3], dtype=int32), this should work  > Index([1, 2, 3], dtype=int32)

Same issue:
```python
pd.Index([1, 2, 3], dtype='int32')
>>> Int64Index([1, 2, 3], dtype='int64')
``` Hm ok, then ea dtypes only Any specific reasons for closing and not merging? Äh no, sorry for that. Pressed the wrong button merged #48106, thx @CloseChoice 