Whisk together the sauce ingredients, adding more salt to taste as this will depend on your mayonnaise.
Remove the woody stem and outer leaves of the cabbage, and slice into small pieces. Wash and slice the celery and grate the carrot. Cut it as chunky or fine as you want, I personally prefer a chunky slaw for added crunch.
Stir through the sauce and refrigerate until ready to serve. I find it usually is best eaten within the first few hours, otherwise the red cabbage and leak out its colour and you have pinkslaw!