API: expose dtypes in pandas.api.types (#16099)

* API: expose dtypes in pandas.api.types

xref #16015
xref apache/arrow#585
xref #16042
xref #15541 (comment)

Author: jreback

pandas/api/types/__init__.py

@@ -1,6 +1,10 @@
 """ public toolkit API """
 
 from pandas.core.dtypes.api import *  # noqa
+from pandas.core.dtypes.dtypes import (CategoricalDtype,  # noqa
+                                       DatetimeTZDtype,
+                                       PeriodDtype,
+                                       IntervalDtype)
 from pandas.core.dtypes.concat import union_categoricals  # noqa
 from pandas._libs.lib import infer_dtype  # noqa
 del np  # noqa

pandas/tests/api/test_types.py

@@ -33,10 +33,12 @@ class TestTypes(Base, tm.TestCase):
                'is_list_like', 'is_hashable',
                'is_named_tuple', 'is_sequence',
                'pandas_dtype', 'union_categoricals', 'infer_dtype']
+    dtypes = ['CategoricalDtype', 'DatetimeTZDtype',
+              'PeriodDtype', 'IntervalDtype']
 
     def test_types(self):
 
-        self.check(types, self.allowed)
+        self.check(types, self.allowed + self.dtypes)
 
     def check_deprecation(self, fold, fnew):
         with tm.assert_produces_warning(DeprecationWarning):