diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index d22b4bd4d3f2b..984f1835bd078 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -89,6 +89,9 @@ def f(self, other):
             return NotImplemented
 
         other = lib.item_from_zerodim(other)
+        if is_list_like(other) and len(other) != len(self):
+            # TODO: Could this fail if the categories are listlike objects?
+            raise ValueError("Lengths must match.")
 
         if not self.ordered:
             if op in ["__lt__", "__gt__", "__le__", "__ge__"]:
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 356ae20b2240a..bd998656914c6 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -48,6 +48,7 @@
 )
 from pandas.core.dtypes.concat import concat_compat
 from pandas.core.dtypes.generic import (
+    ABCCategorical,
     ABCDataFrame,
     ABCDateOffset,
     ABCDatetimeArray,
@@ -99,11 +100,14 @@
 
 def _make_comparison_op(op, cls):
     def cmp_method(self, other):
-        if isinstance(other, (np.ndarray, Index, ABCSeries)):
+        if isinstance(other, (np.ndarray, Index, ABCSeries, ExtensionArray)):
             if other.ndim > 0 and len(self) != len(other):
                 raise ValueError("Lengths must match to compare")
 
-        if is_object_dtype(self) and not isinstance(self, ABCMultiIndex):
+        if is_object_dtype(self) and isinstance(other, ABCCategorical):
+            left = type(other)(self._values, dtype=other.dtype)
+            return op(left, other)
+        elif is_object_dtype(self) and not isinstance(self, ABCMultiIndex):
             # don't pass MultiIndex
             with np.errstate(all="ignore"):
                 result = ops._comp_method_OBJECT_ARRAY(op, self.values, other)
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 0f6aa711adc90..8bfa7e8d20b4f 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -899,31 +899,12 @@ def _make_compare(op):
             opname = "__{op}__".format(op=op.__name__)
 
             def _evaluate_compare(self, other):
-
-                # if we have a Categorical type, then must have the same
-                # categories
-                if isinstance(other, CategoricalIndex):
-                    other = other._values
-                elif isinstance(other, Index):
-                    other = self._create_categorical(other._values, dtype=self.dtype)
-
-                if isinstance(other, (ABCCategorical, np.ndarray, ABCSeries)):
-                    if len(self.values) != len(other):
-                        raise ValueError("Lengths must match to compare")
-
-                if isinstance(other, ABCCategorical):
-                    if not self.values.is_dtype_equal(other):
-                        raise TypeError(
-                            "categorical index comparisons must "
-                            "have the same categories and ordered "
-                            "attributes"
-                        )
-
-                result = op(self.values, other)
+                with np.errstate(all="ignore"):
+                    result = op(self.array, other)
                 if isinstance(result, ABCSeries):
                     # Dispatch to pd.Categorical returned NotImplemented
                     # and we got a Series back; down-cast to ndarray
-                    result = result.values
+                    result = result._values
                 return result
 
             return compat.set_function_name(_evaluate_compare, opname, cls)
diff --git a/pandas/core/ops/__init__.py b/pandas/core/ops/__init__.py
index 4ab1941e3493f..c78d5c79453ab 100644
--- a/pandas/core/ops/__init__.py
+++ b/pandas/core/ops/__init__.py
@@ -1038,8 +1038,14 @@ def wrapper(self, other, axis=None):
             # Defer to DataFrame implementation; fail early
             return NotImplemented
 
-        elif isinstance(other, ABCSeries) and not self._indexed_same(other):
+        if isinstance(other, ABCSeries) and not self._indexed_same(other):
             raise ValueError("Can only compare identically-labeled Series objects")
+        elif (
+            is_list_like(other)
+            and len(other) != len(self)
+            and not isinstance(other, (set, frozenset))
+        ):
+            raise ValueError("Lengths must match")
 
         elif is_categorical_dtype(self):
             # Dispatch to Categorical implementation; CategoricalIndex
diff --git a/pandas/tests/indexes/test_category.py b/pandas/tests/indexes/test_category.py
index 280b0a99c7e68..67bf9bd20e716 100644
--- a/pandas/tests/indexes/test_category.py
+++ b/pandas/tests/indexes/test_category.py
@@ -823,6 +823,11 @@ def test_equals_categorical(self):
         msg = (
             "categorical index comparisons must have the same categories"
             " and ordered attributes"
+            "|"
+            "Categoricals can only be compared if 'categories' are the same. "
+            "Categories are different lengths"
+            "|"
+            "Categoricals can only be compared if 'ordered' is the same"
         )
         with pytest.raises(TypeError, match=msg):
             ci1 == ci2