Functoriality of pullbacks of sets

It seems to me that Peter Freyd remarked it is easy to define pullbacks in ZF (maybe with with global choice?) so that pullback along one side is functorial, but hard to make it functorial on both sides. In other words we can easily make base change functorial in the bases, but not easily make it functorial in the bases at the same time as in the total spaces. Can anyone direct me to a reference to that work? thanks, Colin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]