FOM: On the irrelevance of being well-powered

Vaughan Pratt pratt at cs.Stanford.EDU
Sun Jan 25 02:24:11 EST 1998

Whether a topos is well-powered is equivalent to whether 1 (the final
object) is a generator, i.e. that the functor Hom(1,-) is faithful.
This requirement is at as low a level of logical complexity in the world
of categories as it is at a high level in the world of sets.

Apropos of this, the following post would seem to indicate that being
well-powered is not essential to category theory.  :)
Vaughan Pratt

>Date: Wed, 14 Jan 1998 16:39:27 -0500 (EST)
>From: Michael Barr <barr at>
>To: categories <categories at>
>Subject: Non-well-powered
>As most of you know, we at McGill are offline since about a week.  McGill's
>main computer seems to be online and I was able to telnet to an old account
>I had at Penn.  Anyway, I think we are all well.  I was without power for
>a week (less 4 four hours).  We spent part of that time in my office
>(sleeping bag and couch) and then the power was shut off at McGill (where
>it still is) and we went to the Foxes until we got our power back on 
>Tuesday morning.  We are now back home and everything is back to normal.
>I know there have been some inquiries, whence this note.

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