From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8900 Path: news.gmane.org!not-for-mail From: Paul B Levy Newsgroups: gmane.science.mathematics.categories Subject: free cocompletion Date: Wed, 11 May 2016 14:08:15 +0100 Message-ID: Reply-To: Paul B Levy NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1463008251 9973 80.91.229.3 (11 May 2016 23:10:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 11 May 2016 23:10:51 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Thu May 12 01:10:42 2016 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.22]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1b0dH8-0006Gi-1G for gsmc-categories@m.gmane.org; Thu, 12 May 2016 01:10:42 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:38168) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1b0dGH-0006fw-TB; Wed, 11 May 2016 20:09:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1b0dG8-0005Li-En for categories-list@mlist.mta.ca; Wed, 11 May 2016 20:09:40 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8900 Archived-At: Hi, the following result appears to be folklore: Given a locally small category C, the full subcategory of [C^op,Set] on small presheaves (i.e. those presheaves that are colimits of a small diagram of representables) is a free cocomplete locally small category on C. I've seen and heard this result in many places, and know how to prove it, but is there a proof written out in the literature? And where did the statement first appear? Paul -- Paul Blain Levy School of Computer Science, University of Birmingham http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]