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I am working in ZFC together wit the axiom that every set is element of a Grothendieck universe. So I do not use class choice at all but instead choice in all Grothendieck universes. What I meant is that one should not reduce choice to the first universe but instead have it for all sets irrespective of the universe they live in! I always found this the most convient setting to work in. But not many people do it. But if you work in it then there is no need for class choice anymore. Sorry for not having expanded my general implicit assumptions beforehand. I do see that my view is not the majority view. But it is the most convenient setting for doing category theory in my eyes and it is weaker than real large cardinal axioms that set theorists study consider. Thomas ---------- You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. 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