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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: Fri, 14 Apr 2017 15:55:42 +0200	[thread overview]
Message-ID: <E1cz2NR-0003Ok-FS@mlist.mta.ca> (raw)
In-Reply-To: <E1cyii9-0006vF-Uk@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).

As to (1) even if K = Set we know that the Set^C are ccc's (actually toposes)
but reindexing in general doesn't preserve the ccc's structure since
in Set^C the exponentials are not computed pointwise (unless C is discrete).
It already goes wrong when C is the ordinal 2.

Thomas


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  parent reply	other threads:[~2017-04-14 13:55 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 [this message]
2017-04-16 10:31   ` Thomas Streicher
2017-04-17  0:11   ` Thomas Streicher
2017-04-13 20:00 Ronnie

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