From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9673 Path: news.gmane.org!.POSTED!not-for-mail From: Andrew Pitts Newsgroups: gmane.science.mathematics.categories Subject: Re: Sheaf terminology question Date: Wed, 18 Jul 2018 09:56:22 +0100 Message-ID: References: Reply-To: Andrew Pitts NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 (Mac OS X Mail 11.4 \(3445.8.2\)) Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1531926511 826 195.159.176.226 (18 Jul 2018 15:08:31 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Wed, 18 Jul 2018 15:08:31 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Wed Jul 18 17:08:26 2018 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 1ffo41-00006K-R4 for gsmc-categories@m.gmane.org; Wed, 18 Jul 2018 17:08:25 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:36247) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ffo4l-000876-1x; Wed, 18 Jul 2018 12:09:11 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ffo4A-00055k-K9 for categories-list@mlist.mta.ca; Wed, 18 Jul 2018 12:08:34 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9673 Archived-At: > On 13 Jul 2018, at 15:10, Andrew Pitts = wrote: >=20 > Given a coverage on a small category, the condition for a Set-valued = presheaf on the category to be a sheaf has an existence part and a = uniqueness part. If only the uniqueness part holds, one says that the = presheaf is separated. Is there a name out there for presheaves that = only satisfy the existence part of the sheaf condition? Many thanks to those who responded with suggestions. I won=E2=80=99t = repeat replies that were also sent to categories@mta.ca, but there were = a couple sent privately that I pass on: Peter Johnstone reminded me of the fact that category-theorists tend to = use the prefix =E2=80=9Cweak=E2=80=9D to remove the uniqueness part of a = unique existence condition. So one could speak of "weak sheaves". (A = slight problem with that is that when I say it, it sounds a lot like = wheat sheaves :-).) Tom Hirschowitz pointed out that there is the concept of effective = descent data in stack theory, so one might use the term =E2=80=9Ceffective= presheaf=E2=80=9D for what I was referring to. I quite like that. Andy [For admin and other information see: http://www.mta.ca/~cat-dist/ ]