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In "mathematics in the small", local axiom of choice allows us to choose representatives only when needed. So we are grew up believing that putting things in the definition that are not preserved by morphisms is "not done" (the religious dogma) . But them we run up against issues when we try to do the same thing in "mathematics in the large", and either ignore the problem or argue endlessly about how to solve it. Also, if are willing to assume that every set comes with a well-ordering, why not assume a global well-ordering and be done with it? [If I am going to use universes anyway, it seems to be trivial to do this, as long as I live inside a fixed universe in any given proof.] For ZFC, global choice is a conservative extension. Not being a logician, am not sure, but perhaps it can be shown for global choice is a conservative extension of local choice of 'all suitable set theories'. Then we can do global choice with no qualms. Regards Nath Rao ---------- You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. Leave group: https://outlook.office365.com/owa/categories@mq.edu.au/groupsubscription.as= hx?source=3DEscalatedMessage&action=3Dleave&GuestId=3D4eb9b40c-9b3a-48a5-97= 81-836e5a171e8b