From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2088 Path: news.gmane.org!not-for-mail From: "C.F.Townsend" Newsgroups: gmane.science.mathematics.categories Subject: Naturality of a Change of Base Result Date: Thu, 9 Jan 2003 14:39:27 -0000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" X-Trace: ger.gmane.org 1241018399 2371 80.91.229.2 (29 Apr 2009 15:19:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:19:59 +0000 (UTC) To: "categories@mta.ca" Original-X-From: rrosebru@mta.ca Thu Jan 9 21:16:03 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 09 Jan 2003 21:16:03 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18Wndm-0001ZJ-00 for categories-list@mta.ca; Thu, 09 Jan 2003 21:07:18 -0400 X-Mailer: Internet Mail Service (5.5.2653.19) Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 13 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:2088 Archived-At: Given a geometric morphism n:E->F between Grothendieck toposes (over, say, Set) E is both an F-indexed category and a Set-indexed category. There is the following change of base result for any small (i.e. internal to Set) category C: - The category of F-indexed functors p^*C->E is equivalent to the category of Set-indexed functors C->E (where the first E is as an F-indexed cat and the second as a Set-indexed cat). (And p:F->Set.) Is there anything published/known as to the naturality of this equivalence? It is easy to see that it is natural in functors on C; but I also think (a) that it may be natural with respect to filtred cocontinuous functors between inductive completions of C and (b) between filtered cocontinuous functors on E. Thanks for any thoughts on this technical question, Regards, Christopher Townsend (Open University).