Long story short, I decided to go to get more education (grad school) as a physicist. However, my focus is quantum gravity (always fun stuff when the adjective quantum is being used ) and I need to learn qualitative mathematics.

So my problem is I need to learn qualitative math but I don't have a clue where to begin! I have been told "Topos theory" and "Category theory" are a "good start", but frankly I would like to verify this with a math wizard...someone with experience or knowledge of these things.

Any help would be greatly appreciated!