FOM: On the irrelevance of being well-powered
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. :)
>Date: Wed, 14 Jan 1998 16:39:27 -0500 (EST)
>From: Michael Barr <barr at linc.cis.upenn.edu>
>To: categories <categories at mta.ca>
>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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