I find the nLab entry on the "principle of equivalence" (formerly entitled "evil") hard reading, and in the final end the status of this principle is not at all clear to me.
Is "evil" thinking - of equality between objects - something one only should avoid or something one must avoid (as a categorist/structuralist)? What "happens" when one forgets to avoid it, what can one run into? Into contradictions or only into something hideous or "unnatural"?
Especially: Why is "evil" thinking allowed for skeletal categories?