From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10854 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: ptj@maths.cam.ac.uk Newsgroups: gmane.science.mathematics.categories Subject: Re: Direct image functors Date: 08 Nov 2022 21:36:12 +0000 Message-ID: References: <1C2D2A4F-AFE4-4285-A70A-A77888CFB934@cs.bham.ac.uk> Reply-To: ptj@maths.cam.ac.uk Mime-Version: 1.0 Content-Type: text/plain; format=flowed; charset=ISO-8859-1 Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="29803"; mail-complaints-to="usenet@ciao.gmane.io" Cc: "categories@mta.ca list" To: Steve Vickers Original-X-From: majordomo@rr.mta.ca Thu Nov 10 03:32:01 2022 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.75]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1osxMD-0007K0-IC for gsmc-categories@m.gmane-mx.org; Thu, 10 Nov 2022 03:31:57 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:35188) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1osxLq-00043L-Ae; Wed, 09 Nov 2022 22:31:34 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1osxL2-0000jC-FG for categories-list@rr.mta.ca; Wed, 09 Nov 2022 22:30:44 -0400 In-Reply-To: <1C2D2A4F-AFE4-4285-A70A-A77888CFB934@cs.bham.ac.uk> Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10854 Archived-At: Dear Steve, > By the way, I looked at the Elephant to see what you said there, and I > saw "we shall see later that, in a sense, f_* 'embodies the geometric > aspects' of the morphism f". What did you have in mind for the "we shall > see later"? > I'm not now sure exactly what I meant, but I believe I was thinking primarily of the fact that f_*: Sh(X) --> Sh(Y) points in the same direction as a continuous map f: X --> Y of spaces. On the other hand, my assertion that f^* `embodies the algebraic aspects' of f is certainly explained by A4.1 18 -- the fact that inverse image functors are unital morphisms of geometric allegories. Peter [For admin and other information see: http://www.mta.ca/~cat-dist/ ]