Sure, they are "evil" but it seems to be beneficial to be "evil" sometimes. If the equivalence closed version would have been the original one I doubt that it would have been recognized how useful they are for category theory over fairly general bases. Or, rather, people would have quickly shifted to the "evil" version. BTW under a regime which identifies equality with being isomorphic (or weakly equivalent) it looks tempting to use functors from B^\op to Cat. These should capture the pseudo-functors since equality and isomorphism are identified. But writing down functoriality in type theory using \Sigma for existence amounts to choosing a lot of not at all canonical "canonical isomorphisms". Actually, one would get something even more general than pseudo-functors because one wouldn't write down the coherence conditions (actually one couldn't even since there is no honest for good equality!). Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]