From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9115 Path: news.gmane.org!.POSTED!not-for-mail From: Jean Benabou Newsgroups: gmane.science.mathematics.categories Subject: Weighted limits Date: Mon, 13 Feb 2017 15:41:03 +0100 Message-ID: Reply-To: Jean Benabou NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1487084094 7541 195.159.176.226 (14 Feb 2017 14:54:54 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 14 Feb 2017 14:54:54 +0000 (UTC) To: Categories , Ross Street Original-X-From: majordomo@mlist.mta.ca Tue Feb 14 15:54:48 2017 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 1cdeVE-0001V0-1r for gsmc-categories@m.gmane.org; Tue, 14 Feb 2017 15:54:48 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:43507) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cdeTl-0005eV-4F; Tue, 14 Feb 2017 10:53:17 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cdeTE-0007u2-AR for categories-list@mlist.mta.ca; Tue, 14 Feb 2017 10:52:44 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9115 Archived-At: Dear all, In section B1.1 of the Elephant, weighted limits in a 2-category are defined up to equivalence by pseudo cones. Let me say that strict weighted limits exist if we can replace pseudo cones by genuine cones. These limits are then defined up to a unique isomorphism. In the category CAT of categories (fill in universes if you don't want to run into meta categories) such strict limits exist. Let me say that a 2-category is strictly finitely 2-complete if such strict weighted limits exist for all finite (in an obvious sense) weighted categories. QUESTION: Let S be a category with finite limits. I denote by Cat(S) the 2-category of internal categories of S. Under which conditions on S is Cat(S) strictly finitely 2-complete? Best to all, Jean [For admin and other information see: http://www.mta.ca/~cat-dist/ ]