ASV: Add merge on categorical benchmarks (#45169)

Author: lukemanley

asv_bench/benchmarks/join_merge.py

@@ -262,12 +262,24 @@ def setup(self):
             Z=self.right_object["Z"].astype("category")
         )
 
+        self.left_cat_col = self.left_object.astype({"X": "category"})
+        self.right_cat_col = self.right_object.astype({"X": "category"})
+
+        self.left_cat_idx = self.left_cat_col.set_index("X")
+        self.right_cat_idx = self.right_cat_col.set_index("X")
+
     def time_merge_object(self):
         merge(self.left_object, self.right_object, on="X")
 
     def time_merge_cat(self):
         merge(self.left_cat, self.right_cat, on="X")
 
+    def time_merge_on_cat_col(self):
+        merge(self.left_cat_col, self.right_cat_col, on="X")
+
+    def time_merge_on_cat_idx(self):
+        merge(self.left_cat_idx, self.right_cat_idx, on="X")
+
 
 class MergeOrdered:
     def setup(self):