updated the code in accordance with GH24845

Author: GivyBoy

pandas/core/indexes/category.py

@@ -569,41 +569,14 @@ def map(self, mapper):
         mapped = self._values.map(mapper)
         return Index(mapped, name=self.name)
 
-    def _permutation_check(self, to_concat) -> bool:
-        # GH40378 - we have to check if they are permutations.
-        # If they are, we have to create a fix, in order to
-        # prevent the error discussed in the named issue
-        permutations = True
-        category1 = CategoricalIndex(
-            [],
-            categories=to_concat[0]._is_dtype_compat(to_concat[0]).categories,
-            ordered=False,
-        )
-        for i in to_concat[1:]:
-            category2 = CategoricalIndex(
-                [], categories=i._is_dtype_compat(i).categories, ordered=False
-            )
-            if not category1.equals(category2):
-                permutations = False
-
-        return permutations
-
     def _concat(self, to_concat: list[Index], name: Hashable) -> Index:
         # if calling index is category, don't check dtype of others
 
-        cat_index = True
-
-        for i in to_concat:
-            if not isinstance(i, CategoricalIndex):
-                cat_index = False
-                break
-
         try:
-            if cat_index:
-                if self._permutation_check(to_concat):
-                    raise TypeError
 
-            codes = np.concatenate([self._is_dtype_compat(c).codes for c in to_concat])
+            result = Categorical._concat_same_type(list(to_concat))
+
+            return CategoricalIndex(result, name=name)
 
         except TypeError:
             # not all to_concat elements are among our categories (or NA)
@@ -612,6 +585,3 @@ def _concat(self, to_concat: list[Index], name: Hashable) -> Index:
             res = concat_compat([x._values for x in to_concat])
 
             return Index(res, name=name)
-        else:
-            cat = self._data._from_backing_data(codes)
-            return type(self)._simple_new(cat, name=name)