In a large stainless steel bowl, combine the cabbage, green pepper, onion and carrot, and toss to blend well.
In a separate bowl, blend the sugar, salt, black pepper, mustard, celery seeds and apple cider vinegar.Allow the dressing to marinate for 15 minutes, then whisk in the oil.
Combine the dressing with the tossed vegetables. Blend well. Adjust the salt and pepper to taste.
Refrigerate until needed.