CLN: simplify Categorical comparisons

pandas/core/arrays/categorical.py

@@ -80,17 +80,9 @@ def func(self, other):
             # the same (maybe up to ordering, depending on ordered)
 
             msg = "Categoricals can only be compared if 'categories' are the same."
-            if len(self.categories) != len(other.categories):
-                raise TypeError(msg + " Categories are different lengths")
-            elif self.ordered and not (self.categories == other.categories).all():
-                raise TypeError(msg)
-            elif not set(self.categories) == set(other.categories):
+            if not self.is_dtype_equal(other):
                 raise TypeError(msg)
 
-            if not (self.ordered == other.ordered):
-                raise TypeError(
-                    "Categoricals can only be compared if 'ordered' is the same"
-                )
             if not self.ordered and not self.categories.equals(other.categories):
                 # both unordered and different order
                 other_codes = _get_codes_for_values(other, self.categories)

pandas/tests/arrays/categorical/test_operators.py

@@ -79,18 +79,13 @@ def test_comparisons(self):
 
         cat_rev_base2 = Categorical(["b", "b", "b"], categories=["c", "b", "a", "d"])
 
-        msg = (
-            "Categoricals can only be compared if 'categories' are the same. "
-            "Categories are different lengths"
-        )
         with pytest.raises(TypeError, match=msg):
             cat_rev > cat_rev_base2
 
         # Only categories with same ordering information can be compared
         cat_unorderd = cat.set_ordered(False)
         assert not (cat > cat).any()
 
-        msg = "Categoricals can only be compared if 'ordered' is the same"
         with pytest.raises(TypeError, match=msg):
             cat > cat_unorderd
 
@@ -321,7 +316,7 @@ def test_compare_different_lengths(self):
         c1 = Categorical([], categories=["a", "b"])
         c2 = Categorical([], categories=["a"])
 
-        msg = "Categories are different lengths"
+        msg = "Categoricals can only be compared if 'categories' are the same."
         with pytest.raises(TypeError, match=msg):
             c1 == c2
 

pandas/tests/indexes/categorical/test_category.py

@@ -402,15 +402,7 @@ def test_equals_categorical(self):
         with pytest.raises(ValueError, match="Lengths must match"):
             ci1 == Index(["a", "b", "c"])
 
-        msg = (
-            "categorical index comparisons must have the same categories "
-            "and ordered attributes"
-            "|"
-            "Categoricals can only be compared if 'categories' are the same. "
-            "Categories are different lengths"
-            "|"
-            "Categoricals can only be compared if 'ordered' is the same"
-        )
+        msg = "Categoricals can only be compared if 'categories' are the same"
         with pytest.raises(TypeError, match=msg):
             ci1 == ci2
         with pytest.raises(TypeError, match=msg):