Re: size_question_encore

[Toby Bartels <categories@TobyBartels.name>]

Mike Shulman wrote in part:

>Even in a category of sets, I don't see why choice is necessary in
>order to complete a small subcategory under finite limits and obtain a
>small subcategory.  It seems to me that what is needed is rather the
>axiom of collection, which implies that we can find some *set* of
>objects containing *at least one* limit for every finite diagram in
>the original small subcategory; and then we can iterate countably many
>times to obtain a small category which contains at least one limit for
>any finite diagram therein.

The axiom of collection guarantees only *some* appropriate set of objects,
so you need to choose one.  To iterate this countably many times,
you might need dependent choice.

Unless I'm not understanding what you're doing.


--Toby


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