From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1517 Path: news.gmane.org!not-for-mail From: grandis@dima.unige.it (Marco Grandis) Newsgroups: gmane.science.mathematics.categories Subject: Finitely presentable presheaves Date: Tue, 16 May 2000 16:55:28 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241017893 31617 80.91.229.2 (29 Apr 2009 15:11:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:11:33 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue May 16 12:57:33 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id MAA07941 for categories-list; Tue, 16 May 2000 12:57:26 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:1517 Archived-At: Consider the category of presheaves C^ on a small category, C. Plainly, a finite colimit F of representables presheaves is finitely presentable, in the usual sense: C^(F, -) preserves filtered colimits. But the converse is also true and seemingly well known: every finitely presentable presheaf is a finite colimit of representables. Is this proved somewhere? Best regards Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/STAFF/GRANDIS/ ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/