From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/10138 Path: news.gmane.io!.POSTED.ciao.gmane.io!not-for-mail From: Redi Haderi Newsgroups: gmane.science.mathematics.categories Subject: Interpreting category-valued presheaves Date: Sat, 15 Feb 2020 22:11:50 +0300 Message-ID: Reply-To: Redi Haderi Mime-Version: 1.0 Content-Type: text/plain; charset="UTF-8" Injection-Info: ciao.gmane.io; posting-host="ciao.gmane.io:159.69.161.202"; logging-data="26546"; mail-complaints-to="usenet@ciao.gmane.io" To: categories@mta.ca Original-X-From: majordomo@rr.mta.ca Sun Feb 16 17:30:28 2020 Return-path: Envelope-to: gsmc-categories@m.gmane-mx.org Original-Received: from smtp2.mta.ca ([198.164.44.55]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1j3MoO-0006nc-2h for gsmc-categories@m.gmane-mx.org; Sun, 16 Feb 2020 17:30:28 +0100 Original-Received: from rr.mta.ca ([198.164.44.159]:44614) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1j3Mlq-00030G-3Y; Sun, 16 Feb 2020 12:27:50 -0400 Original-Received: from majordomo by rr.mta.ca with local (Exim 4.92.1) (envelope-from ) id 1j3Mmc-00089f-JN for categories-list@rr.mta.ca; Sun, 16 Feb 2020 12:28:38 -0400 Precedence: bulk Xref: news.gmane.io gmane.science.mathematics.categories:10138 Archived-At: Dear categorists, I could not find an answer to the following, so I need your help: Given a category C we know that the category of set-valued presheaves on C may be interpreted as a free cocompletion of C. More precisely, if we denote PSh(C) the presheaf category, then colimit-preserving functors from PSh(C) to a cocomplete category D correspond to functors from C to D (via Yoneda extension). I am interested in an interpretation of category-valued presheaves. Is there some sort of 2-categorical version of the above fact? Best regards, Redi Haderi [For admin and other information see: http://www.mta.ca/~cat-dist/ ]