BUG: set_levels not preserving categorical (#52177)

* BUG: set_levels not preserving categorical

* Fix

Author: phofl

doc/source/whatsnew/v2.1.0.rst

@@ -200,7 +200,7 @@ Missing
 
 MultiIndex
 ^^^^^^^^^^
--
+- Bug in :meth:`MultiIndex.set_levels` not preserving dtypes for :class:`Categorical` (:issue:`52125`)
 -
 
 I/O

pandas/core/indexes/multi.py

@@ -73,6 +73,7 @@
     ABCDatetimeIndex,
     ABCTimedeltaIndex,
 )
+from pandas.core.dtypes.inference import is_array_like
 from pandas.core.dtypes.missing import (
     array_equivalent,
     isna,
@@ -945,7 +946,11 @@ def set_levels(
         FrozenList([['a', 'b', 'c'], [1, 2, 3, 4]])
         """
 
-        if is_list_like(levels) and not isinstance(levels, Index):
+        if isinstance(levels, Index):
+            pass
+        elif is_array_like(levels):
+            levels = Index(levels)
+        elif is_list_like(levels):
             levels = list(levels)
 
         level, levels = _require_listlike(level, levels, "Levels")

pandas/tests/indexes/multi/test_get_set.py

@@ -367,3 +367,11 @@ def test_set_levels_pos_args_removal():
 
     with pytest.raises(TypeError, match="positional arguments"):
         idx.set_codes([[0, 1], [1, 0]], 0)
+
+
+def test_set_levels_categorical_keep_dtype():
+    # GH#52125
+    midx = MultiIndex.from_arrays([[5, 6]])
+    result = midx.set_levels(levels=pd.Categorical([1, 2]), level=0)
+    expected = MultiIndex.from_arrays([pd.Categorical([1, 2])])
+    tm.assert_index_equal(result, expected)