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
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev 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
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1cz2NR-0003Ok-FS@mlist.mta.ca \
--to=streicher@mathematik.tu-darmstadt.de \
--cc=categories@mta.ca \
--cc=gaucher@irif.fr \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).