categories: Re: Is Set lfp, intuitionistically?

["Dr. P.T. Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk>]

On Mon, 1 Oct 2001, Michael Abbott wrote:

> Or, I hope this is the same question, is an elementary topos with a natural
> numbers object internally locally finitely presentable?  Are there any
> references for this?
>
The answer is yes, but (like a great many such things) I don't think
it is written down anywhere. Finite cardinals are internally finitely
presentable (the proof of this is similar to the proof that they are
internally projective, see 6.25 in "Topos Theory"), and the fact that
every object is internally a filtered colimit of finite cardinals
is implicit in the construction of the object classifier (cf. 6.32
in the same reference).

Peter Johnstone