How should we type `Series` with a categorical dtype?

[cmp0xff]

After #1383 and #1391, pd.Series([1], dtype="category") gives Series[CategoricalDtype].

Is it the best idea to follow? Typically we use the type of elements as the Generic type of a Series or Index, for example Series[int], instead of Series[Int64Dtype]. The current approach seems inconsistent to me.

This is also related to #1395, where

• Series([1], dtype=int): dtype is np.dtype("int64"), element type is np.int64. Currently this is Series[int] in pandas-stubs.
• Series([1], dtype="Int64"): dtype is pd.Int64Dtype, element type is (built-in) int. Currently this is Series[Any] in pandas-stubs.

We will discuss the last part in #1395, here it is just an illustrative example.

[Dr-Irv]

For categorical series, one option we have here is to not use CategoricalDtype in SeriesDTypeNoDateTime, but instead use Literal["category"] . Or, we could do something like we do with Interval, where we create a new class CategoricalItem[C1], where C1 is int, float, str , object .