Core the cabbage, and cut into pieces that will fit into the chute of your food processor.
Shred the cabbage with the food processor.
Peel the carrot, and shred with the food processor. Core the pepper, and shred it as well.
Mix the sugar, oil, vinegar, celery seed, and salt together in the bottom of a large bowl.
Add the shredded cabbage, red peppers, and carrots, and stir to combine.
Season with more salt if needed. Serve immediately.
Notes
If you do not have a food processor, you can grate the vegetables with a box grater, or use a mandolin.You could also finely slice the cabbage with a sharp knife, but the food processor or grater is best so that it's really nicely shredded.Store leftovers in the refrigerator. They should stay fresh for about 5 days.