GH31581 adding regression test (#52740)

Author: corriebar

pandas/tests/frame/indexing/test_setitem.py

@@ -1263,6 +1263,17 @@ def test_setitem_column_update_inplace(self, using_copy_on_write):
             # original dataframe not updated
             assert np.all(values[np.arange(10), np.arange(10)] == 0)
 
+    def test_setitem_column_frame_as_category(self):
+        # GH31581
+        df = DataFrame([1, 2, 3])
+        df["col1"] = DataFrame([1, 2, 3], dtype="category")
+        df["col2"] = Series([1, 2, 3], dtype="category")
+
+        expected_types = Series(
+            ["int64", "category", "category"], index=[0, "col1", "col2"]
+        )
+        tm.assert_series_equal(df.dtypes, expected_types)
+
     @pytest.mark.parametrize("dtype", ["int64", "Int64"])
     def test_setitem_iloc_with_numpy_array(self, dtype):
         # GH-33828