From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9182 Path: news.gmane.org!.POSTED!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: About the cartesian closedness of the category of all small diagrams Date: Fri, 14 Apr 2017 15:55:42 +0200 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: blaine.gmane.org 1492180785 30371 195.159.176.226 (14 Apr 2017 14:39:45 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Fri, 14 Apr 2017 14:39:45 +0000 (UTC) Cc: categories@mta.ca To: gaucher Original-X-From: majordomo@mlist.mta.ca Fri Apr 14 16:39:40 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1cz2Nu-0007mJ-Qn for gsmc-categories@m.gmane.org; Fri, 14 Apr 2017 16:39:38 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:40949) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cz2O6-0003ZD-Py; Fri, 14 Apr 2017 11:39:50 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cz2NR-0003Ok-FS for categories-list@mlist.mta.ca; Fri, 14 Apr 2017 11:39:09 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9182 Archived-At: 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/ ]