diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 5274213f114e3..6f3c1561ff5db 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -12,6 +12,7 @@
 from pandas._libs.tslibs import OutOfBoundsDatetime, Timestamp
 from pandas._libs.tslibs.period import IncompatibleFrequency
 from pandas._libs.tslibs.timezones import tz_compare
+from pandas._typing import Label
 from pandas.compat import set_function_name
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import Appender, Substitution, cache_readonly
@@ -243,7 +244,7 @@ def _outer_indexer(self, left, right):
     _typ = "index"
     _data: Union[ExtensionArray, np.ndarray]
     _id = None
-    _name: Optional[Hashable] = None
+    _name: Label = None
     # MultiIndex.levels previously allowed setting the index name. We
     # don't allow this anymore, and raise if it happens rather than
     # failing silently.
@@ -4126,7 +4127,7 @@ def _assert_can_do_op(self, value):
             raise TypeError(f"'value' must be a scalar, passed: {type(value).__name__}")
 
     @property
-    def _has_complex_internals(self):
+    def _has_complex_internals(self) -> bool:
         """
         Indicates if an index is not directly backed by a numpy array
         """
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 1a53596fb5967..235d1856a2d0b 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -172,6 +172,7 @@ class CategoricalIndex(ExtensionIndex, accessor.PandasDelegate):
 
     codes: np.ndarray
     categories: Index
+    _data: Categorical
 
     @property
     def _engine_type(self):
@@ -312,7 +313,7 @@ def _is_dtype_compat(self, other) -> bool:
 
         return other
 
-    def equals(self, other):
+    def equals(self, other) -> bool:
         """
         Determine if two CategoricalIndex objects contain the same elements.
 
@@ -381,7 +382,7 @@ def values(self):
         return self._data
 
     @property
-    def _has_complex_internals(self):
+    def _has_complex_internals(self) -> bool:
         # used to avoid libreduction code paths, which raise or require conversion
         return True
 
@@ -851,12 +852,12 @@ def _concat_same_dtype(self, to_concat, name):
         result.name = name
         return result
 
-    def _delegate_property_get(self, name, *args, **kwargs):
+    def _delegate_property_get(self, name: str, *args, **kwargs):
         """ method delegation to the ._values """
         prop = getattr(self._values, name)
         return prop  # no wrapping for now
 
-    def _delegate_method(self, name, *args, **kwargs):
+    def _delegate_method(self, name: str, *args, **kwargs):
         """ method delegation to the ._values """
         method = getattr(self._values, name)
         if "inplace" in kwargs:
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index b87dd0f02252f..0f385d9aba9c5 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -2,7 +2,7 @@
 Base and utility classes for tseries type pandas objects.
 """
 import operator
-from typing import Any, List, Optional, Set
+from typing import Any, List, Optional, Set, Union
 
 import numpy as np
 
@@ -31,7 +31,7 @@
 
 from pandas.core import algorithms
 from pandas.core.accessor import PandasDelegate
-from pandas.core.arrays import DatetimeArray, ExtensionArray, TimedeltaArray
+from pandas.core.arrays import DatetimeArray, PeriodArray, TimedeltaArray
 from pandas.core.arrays.datetimelike import DatetimeLikeArrayMixin
 from pandas.core.base import _shared_docs
 import pandas.core.indexes.base as ibase
@@ -90,7 +90,7 @@ class DatetimeIndexOpsMixin(ExtensionIndex):
     Common ops mixin to support a unified interface datetimelike Index.
     """
 
-    _data: ExtensionArray
+    _data: Union[DatetimeArray, TimedeltaArray, PeriodArray]
     freq: Optional[DateOffset]
     freqstr: Optional[str]
     _resolution: int
@@ -468,7 +468,7 @@ def where(self, cond, other=None):
         result = np.where(cond, values, other).astype("i8")
         return self._shallow_copy(result)
 
-    def _summary(self, name=None):
+    def _summary(self, name=None) -> str:
         """
         Return a summarized representation.
 
@@ -955,7 +955,7 @@ class DatetimelikeDelegateMixin(PandasDelegate):
     _raw_methods: Set[str] = set()
     # raw_properties : dispatch properties that shouldn't be boxed in an Index
     _raw_properties: Set[str] = set()
-    _data: ExtensionArray
+    _data: Union[DatetimeArray, TimedeltaArray, PeriodArray]
 
     def _delegate_property_get(self, name, *args, **kwargs):
         result = getattr(self._data, name)
@@ -963,7 +963,7 @@ def _delegate_property_get(self, name, *args, **kwargs):
             result = Index(result, name=self.name)
         return result
 
-    def _delegate_property_set(self, name, value, *args, **kwargs):
+    def _delegate_property_set(self, name: str, value, *args, **kwargs):
         setattr(self._data, name, value)
 
     def _delegate_method(self, name, *args, **kwargs):
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 3afd1ff35806d..4e5e9fa0758c6 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -218,6 +218,7 @@ class DatetimeIndex(DatetimeTimedeltaMixin, DatetimeDelegateMixin):
     _is_numeric_dtype = False
     _infer_as_myclass = True
 
+    _data: DatetimeArray
     tz: Optional[tzinfo]
 
     # --------------------------------------------------------------------
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 26b64836172fd..b7edb1c3bcbca 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -405,7 +405,7 @@ def values(self):
         return self._data
 
     @property
-    def _has_complex_internals(self):
+    def _has_complex_internals(self) -> bool:
         # used to avoid libreduction code paths, which raise or require conversion
         return True
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 5a9825d58b204..02db7be1ddf41 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1347,7 +1347,7 @@ def values(self):
         return self._tuples
 
     @property
-    def _has_complex_internals(self):
+    def _has_complex_internals(self) -> bool:
         # used to avoid libreduction code paths, which raise or require conversion
         return True
 
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 1257e410b4125..45afdaf33421d 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -135,6 +135,8 @@ class TimedeltaIndex(
     _is_numeric_dtype = True
     _infer_as_myclass = True
 
+    _data: TimedeltaArray
+
     # -------------------------------------------------------------------
     # Constructors