/sci/ - Science & Math

>>12192526
>You'll find more details in his book, "Set Theory".
Erm, yes I know what classes are. But good to make sure we read about the same thing I guess.

Again, I don't recall people doing category theory stuff actually actively considering themself to work in ZF while modeling categories as classes. At the very least when you speak of the category of categories CAT, it's clear that the class of all group is not a member of CAT, which would be a big defect of the class approach.
I don't know who they are.

But I'm sure you find it in the Shulman paper and book I cited.

>>12192550
>ZFC_M
If you can gauge how deep your biggest objects are, then you can indeed just take a set in the von Neumann hierarchy. [math]V_{\omega+\omega}[/math] is a model of ZFC and even a topos.
If you use free constructions making use of Replacement, you'll however scale up quite fast.
In case you need all ordinals, which form a class, then you also need more.

>>12192560
>>12192563
>I want to know how much all these books are wrong
I think Colin McLarty is someone who tried to properly research this (e.g. "are ZF universes necessary to formalize the proof of Fermats last theorem, and why not")

If Jech makes a side remark that all you need to do for category theory is classes, then it's fair and good to question that claim.
They are not necessarily experts in all things logic.
You can also find David Hemkins on MO trip over the fact that assuming that ordinals are linearly ordered implies excluded middle, and off-classic-set-theory things like that.