add test for "Allow definition of pd.CategoricalDtype with a specific categories.dtype"

pandas/core/dtypes/dtypes.py

@@ -175,6 +175,8 @@ class CategoricalDtype(PandasExtensionDtype, ExtensionDtype):
     ----------
     categories : sequence, optional
         Must be unique, and must not contain any nulls.
+        The categories are stored in an Index,
+        and if an index is provided the dtype of that index will be used.
     ordered : bool or None, default False
         Whether or not this categorical is treated as a ordered categorical.
         None can be used to maintain the ordered value of existing categoricals when
@@ -210,6 +212,12 @@ class CategoricalDtype(PandasExtensionDtype, ExtensionDtype):
     3    NaN
     dtype: category
     Categories (2, object): [b < a]
+
+    An empty CategoricalDtype with a specific dtype can be created
+    by providing an empty index. As follows,
+
+    >>> pd.CategoricalDtype(pd.DatetimeIndex([])).categories.dtype
+    dtype('<M8[ns]')
     """
 
     # TODO: Document public vs. private API

pandas/tests/dtypes/test_dtypes.py

@@ -26,7 +26,14 @@
 )
 
 import pandas as pd
-from pandas import Categorical, CategoricalIndex, IntervalIndex, Series, date_range
+from pandas import (
+    Categorical,
+    CategoricalIndex,
+    DatetimeIndex,
+    IntervalIndex,
+    Series,
+    date_range,
+)
 import pandas._testing as tm
 from pandas.core.arrays.sparse import SparseArray, SparseDtype
 
@@ -172,6 +179,11 @@ def test_is_boolean(self, categories, expected):
         assert is_bool_dtype(cat) is expected
         assert is_bool_dtype(cat.dtype) is expected
 
+    def test_dtype_specific_categorical_dtype(self):
+        expected = "datetime64[ns]"
+        result = str(Categorical(DatetimeIndex([])).categories.dtype)
+        assert result == expected
+
 
 class TestDatetimeTZDtype(Base):
     @pytest.fixture