From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: gaucher <gaucher@irif.fr>
Cc: categories@mta.ca
Subject: Re: About the cartesian closedness of the category of all small diagrams
Date: Mon, 17 Apr 2017 02:11:46 +0200 [thread overview]
Message-ID: <E1d09rY-0002iR-Bk@mlist.mta.ca> (raw)
In-Reply-To: <E1cz2NR-0003Ok-FS@mlist.mta.ca>
> For a fibration of ccc's over a ccc one knows that the total category
> is again ccc and this structure is preserved (could be in Bart Jacob's book).
This is wrong! Let EE be the free topos (with nno). Then the
fibration Fam(EE) over Set is a fibered ccc but if it were a cartesian
closed functor between toposes then EE would have small sums which it hasn't.
It is not clear at all which fibrations of ccc's over ccc's have the
property that they are ccc-preserving functors between ccc's. It seems
as if such fibrations have to be internally complete. That's what I
definitely overlooked.
Sorry for that,
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2017-04-17 0:11 UTC|newest]
Thread overview: 6+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-04-13 14:13 gaucher
2017-04-14 4:01 ` Ross Street
2017-04-14 13:55 ` Thomas Streicher
2017-04-16 10:31 ` Thomas Streicher
2017-04-17 0:11 ` Thomas Streicher [this message]
2017-04-13 20:00 Ronnie
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