From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9247 Path: news.gmane.org!.POSTED!not-for-mail From: Luc Pellissier Newsgroups: gmane.science.mathematics.categories Subject: Re: Functors arising from a relational Grothendieck construction Date: Fri, 23 Jun 2017 15:56:54 +0200 Message-ID: References: Reply-To: Luc Pellissier NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 (Mac OS X Mail 10.3 \(3273\)) Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1498594240 19668 195.159.176.226 (27 Jun 2017 20:10:40 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 27 Jun 2017 20:10:40 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue Jun 27 22:10:33 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 1dPwof-0004Ty-7S for gsmc-categories@m.gmane.org; Tue, 27 Jun 2017 22:10:29 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:48527) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dPwoy-00020A-6U; Tue, 27 Jun 2017 17:10:48 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dPwnc-0006hR-9k for categories-list@mlist.mta.ca; Tue, 27 Jun 2017 17:09:24 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9247 Archived-At: Thank you all for your answers. I didn't know about Conduch=C3=A9 functors, and what I am looking at are = indeed a relaxed variant where all unicity conditions are dropped. The equivalence arising from the Grothendieck construction I am = interested in is a variant of the one in (Nielsen 2004, TAC 12(7), pp 248=E2=80=93261), = but considering more general natural transformations between relational presheaves (and = not only functional natural transformations). The conditions I have given in my = previous email are the weak factorization lifting property (WFLP) and the = discreteness of fibers in this article. > Le 17 juin 2017 =C3=A0 11:27, Thomas Streicher = a =C3=A9crit : >=20 > I have noticed that, obviously, 2-valued distributors are not closed > under composition in Set-valued distributors. The reason is that in > the latter case the existential quantifier in composition of relations > is understood in a proof relevant way. > So I really don't understand what you mean by Grothendieck > construction applied to a presheaf taking vaues in Rel. Dear Thomas, I use =E2=80=9CGrothendieck construction=E2=80=9D =E2=80=93 very = naively, maybe! =E2=80=93 as a shorthand for =E2=80=9Cpullback of a functor along the forgetful functor of a category = of pointed objects to the category of base objects=E2=80=9D, that is, given a = category BB of base objects, and a category BB* of pointed objects, the pullback of a = functor C -> BB in the situation BB* | | | v C ---> BB When BB =3D Set, and BB* is the category of pointed sets, pullbacks of = this form are discrete fibrations; when BB =3D Cat, pullbacks of this form are = Grothendieck fibrations; and I am interested in the case BB =3D Rel, the category of = sets and relations. Is that any clearer? If I am using the term too naively, I = would be very interested to have a more correct one. =E2=80=94 Luc= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]