Add the cabbage to the food processor about 1 cup at a time and process until finely chopped.
Once you've processed all the cabbage add the onion and carrot to the processor and chop fine.
Mix the cabbage, onion and carrot in a medium bowl.
Add in the mayonnaise, apple cider vinegar, sugar and salt and pepper.
Mix until all ingredients are completely combined.
Refrigerate for a couple hours to chill and let the flavors blend together.
Enjoy!