diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 7c1e95e12d339..477db9b0dc8d7 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -428,19 +428,6 @@ def _engine(self):
         codes = self.codes
         return self._engine_type(lambda: codes, len(self))
 
-    # introspection
-    @cache_readonly
-    def is_unique(self) -> bool:
-        return self._engine.is_unique
-
-    @property
-    def is_monotonic_increasing(self):
-        return self._engine.is_monotonic_increasing
-
-    @property
-    def is_monotonic_decreasing(self) -> bool:
-        return self._engine.is_monotonic_decreasing
-
     @Appender(_index_shared_docs["index_unique"] % _index_doc_kwargs)
     def unique(self, level=None):
         if level is not None:
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index d33ba52cc7524..1c86235f9eaa1 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -437,22 +437,8 @@ def memory_usage(self, deep: bool = False) -> int:
         # so return the bytes here
         return self.left.memory_usage(deep=deep) + self.right.memory_usage(deep=deep)
 
-    @cache_readonly
-    def is_monotonic(self) -> bool:
-        """
-        Return True if the IntervalIndex is monotonic increasing (only equal or
-        increasing values), else False
-        """
-        return self.is_monotonic_increasing
-
-    @cache_readonly
-    def is_monotonic_increasing(self) -> bool:
-        """
-        Return True if the IntervalIndex is monotonic increasing (only equal or
-        increasing values), else False
-        """
-        return self._engine.is_monotonic_increasing
-
+    # IntervalTree doesn't have a is_monotonic_decreasing, so have to override
+    #  the Index implemenation
     @cache_readonly
     def is_monotonic_decreasing(self) -> bool:
         """