The recent discussion of sets against categories on the internet appears to miss the appropriate sources. It is well known that it is easy to go from sets to categories, harder in the reverse. For this there is a very well-known equicoherence theorem, which is presented in both the standard texts on topos Johnstone, Chapter 9, S 7 Mac Lane / Moerdijk (Sheaves in Geometry and Logic, Chapter 6, S 10.) I fondly imagine that the latter is a bit clearer. Both sources will give your the original literature--for example Mitchell JPAA 2(1972) p. 261 (I suggested this question to Bill Mitchell when he was an instructor at Chicago). As far as I can make out; none of the many messages speaks to this fact. It is a reasonable question for Pratt to raise, though he should have known that the Goldblatt book was hopeless from day one. Of course most mathematicians find sets easier than cats--but they usually can't recite ZFC axioms. The fault may lie with Pat Suppes, who taught sets in the Kindergarten. Otherwise, the exchange convinces me tht e-mail is for the birds. All fluff with no professional substance Saunders Mac Lane Department of Mathematics University of Chicago saunders@math.uchicago.edu