diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 4fa6b73932aa4..27e0a198b62a2 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -1376,7 +1376,7 @@ def value_counts(self, dropna=True):
             count = np.bincount(np.where(mask, code, ncat))
             ix = np.append(ix, -1)
 
-        ix = self._constructor(ix, dtype=self.dtype, fastpath=True)
+        ix = self._from_backing_data(ix)
 
         return Series(count, index=CategoricalIndex(ix), dtype="int64")
 
@@ -1546,9 +1546,8 @@ def sort_values(
         if inplace:
             self._codes = self._codes[sorted_idx]
         else:
-            return self._constructor(
-                values=self._codes[sorted_idx], dtype=self.dtype, fastpath=True
-            )
+            codes = self._codes[sorted_idx]
+            return self._from_backing_data(codes)
 
     def _values_for_rank(self):
         """
@@ -1583,7 +1582,7 @@ def _values_for_rank(self):
     def view(self, dtype=None):
         if dtype is not None:
             raise NotImplementedError(dtype)
-        return self._constructor(values=self._codes, dtype=self.dtype, fastpath=True)
+        return self._from_backing_data(self._ndarray)
 
     def to_dense(self):
         """
@@ -1691,7 +1690,7 @@ def fillna(self, value=None, method=None, limit=None):
                     f"or Series, but you passed a {type(value).__name__}"
                 )
 
-        return self._constructor(codes, dtype=self.dtype, fastpath=True)
+        return self._from_backing_data(codes)
 
     # ------------------------------------------------------------------
     # NDArrayBackedExtensionArray compat
@@ -2098,7 +2097,7 @@ def mode(self, dropna=True):
             good = self._codes != -1
             codes = self._codes[good]
         codes = sorted(htable.mode_int64(ensure_int64(codes), dropna))
-        return self._constructor(values=codes, dtype=self.dtype, fastpath=True)
+        return self._from_backing_data(codes)
 
     # ------------------------------------------------------------------
     # ExtensionArray Interface
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 19a0910a7a282..85ef3e58576e3 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -211,29 +211,6 @@ def __new__(
 
         return cls._simple_new(data, name=name)
 
-    def _create_from_codes(self, codes, dtype=None, name=None):
-        """
-        *this is an internal non-public method*
-
-        create the correct categorical from codes
-
-        Parameters
-        ----------
-        codes : new codes
-        dtype: CategoricalDtype, defaults to existing
-        name : optional name attribute, defaults to existing
-
-        Returns
-        -------
-        CategoricalIndex
-        """
-        if dtype is None:
-            dtype = self.dtype
-        if name is None:
-            name = self.name
-        cat = Categorical.from_codes(codes, dtype=dtype)
-        return CategoricalIndex(cat, name=name)
-
     @classmethod
     def _simple_new(cls, values: Categorical, name: Label = None):
         assert isinstance(values, Categorical), type(values)
@@ -495,7 +472,8 @@ def reindex(self, target, method=None, level=None, limit=None, tolerance=None):
 
                 codes = new_target.codes.copy()
                 codes[indexer == -1] = cats[missing]
-                new_target = self._create_from_codes(codes)
+                cat = self._data._from_backing_data(codes)
+                new_target = type(self)._simple_new(cat, name=self.name)
 
         # we always want to return an Index type here
         # to be consistent with .reindex for other index types (e.g. they don't
@@ -695,7 +673,9 @@ def delete(self, loc):
         -------
         new_index : Index
         """
-        return self._create_from_codes(np.delete(self.codes, loc))
+        codes = np.delete(self.codes, loc)
+        cat = self._data._from_backing_data(codes)
+        return type(self)._simple_new(cat, name=self.name)
 
     def insert(self, loc: int, item):
         """
@@ -720,15 +700,14 @@ def insert(self, loc: int, item):
 
         codes = self.codes
         codes = np.concatenate((codes[:loc], [code], codes[loc:]))
-        return self._create_from_codes(codes)
+        cat = self._data._from_backing_data(codes)
+        return type(self)._simple_new(cat, name=self.name)
 
     def _concat(self, to_concat, name):
         # if calling index is category, don't check dtype of others
         codes = np.concatenate([self._is_dtype_compat(c).codes for c in to_concat])
-        result = self._create_from_codes(codes, name=name)
-        # if name is None, _create_from_codes sets self.name
-        result.name = name
-        return result
+        cat = self._data._from_backing_data(codes)
+        return type(self)._simple_new(cat, name=name)
 
     def _delegate_method(self, name: str, *args, **kwargs):
         """ method delegation to the ._values """