From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on inbox.vuxu.org X-Spam-Level: * X-Spam-Status: No, score=1.2 required=5.0 tests=DATE_IN_PAST_24_48, LOCALPART_IN_SUBJECT,RCVD_IN_MSPIKE_H2 autolearn=no autolearn_force=no version=3.4.4 Received: (qmail 7879 invoked from network); 1 Feb 2023 01:12:20 -0000 Received: from smtp2.mta.ca (198.164.44.75) by inbox.vuxu.org with ESMTPUTF8; 1 Feb 2023 01:12:20 -0000 Received: from rr.mta.ca ([198.164.44.159]:40620) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1pN1ff-0005Ew-5x; Tue, 31 Jan 2023 21:12:19 -0400 Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1pN1f5-0002wu-Ta for categories-list@rr.mta.ca; Tue, 31 Jan 2023 21:11:43 -0400 References: From: Richard Garner To: categories@mta.ca Subject: categories: Re: Sheaves as a localisation of separated presheaves Date: Tue, 31 Jan 2023 09:53:30 +1100 MIME-Version: 1.0 Precedence: bulk Reply-To: Richard Garner Message-Id: > the localisation functor Psh(C) --> Psh(C)[D^-1], which obviously > preserves colimits, Here it is perhaps better to say "which does not obviously preserve colimits". But the point remains the same: Psh(C) --> Psh(C)[D^-1] is localisation in the wrong 2-category, CAT rather than COCTS. Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]