BUG: assert_frame_equal still checks category dtypes even when asked not to check index type (#52216)

* Added check_categorical argument in assert_index_equal recursive call

* Added test cases

* Added whatsnew entry and mentioned issue number for test

Author: jayendra-patil33

doc/source/whatsnew/v2.1.0.rst

@@ -274,6 +274,7 @@ Other
 ^^^^^
 - Bug in :func:`assert_almost_equal` now throwing assertion error for two unequal sets (:issue:`51727`)
 - Bug in :meth:`Series.memory_usage` when ``deep=True`` throw an error with Series of objects and the returned value is incorrect, as it does not take into account GC corrections (:issue:`51858`)
+- Bug in :func:`assert_frame_equal` checks category dtypes even when asked not to check index type (:issue:`52126`)
 
 .. ***DO NOT USE THIS SECTION***
 

pandas/_testing/asserters.py

@@ -300,6 +300,7 @@ def _get_ilevel_values(index, level):
                 exact=exact,
                 check_names=check_names,
                 check_exact=check_exact,
+                check_categorical=check_categorical,
                 rtol=rtol,
                 atol=atol,
                 obj=lobj,

pandas/tests/util/test_assert_index_equal.py

@@ -299,3 +299,17 @@ def test_assert_ea_index_equal_non_matching_na(check_names, check_categorical):
         tm.assert_index_equal(
             idx1, idx2, check_names=check_names, check_categorical=check_categorical
         )
+
+
+@pytest.mark.parametrize("check_categorical", [True, False])
+def test_assert_multi_index_dtype_check_categorical(check_categorical):
+    # GH#52126
+    idx1 = MultiIndex.from_arrays([Categorical(np.array([1, 2], dtype=np.uint64))])
+    idx2 = MultiIndex.from_arrays([Categorical(np.array([1, 2], dtype=np.int64))])
+    if check_categorical:
+        with pytest.raises(
+            AssertionError, match=r"^MultiIndex level \[0\] are different"
+        ):
+            tm.assert_index_equal(idx1, idx2, check_categorical=check_categorical)
+    else:
+        tm.assert_index_equal(idx1, idx2, check_categorical=check_categorical)