From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9232 Path: news.gmane.org!.POSTED!not-for-mail From: Luc Pellissier Newsgroups: gmane.science.mathematics.categories Subject: Functors arising from a relational Grothendieck construction Date: Mon, 12 Jun 2017 11:37:45 +0200 Message-ID: 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 1497400354 18367 195.159.176.226 (14 Jun 2017 00:32:34 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Wed, 14 Jun 2017 00:32:34 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Jun 14 02:32:25 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 1dKwET-0004Cb-9m for gsmc-categories@m.gmane.org; Wed, 14 Jun 2017 02:32:25 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60446) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dKwED-0005FR-JS; Tue, 13 Jun 2017 21:32:09 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dKwD6-0000jU-1e for categories-list@mlist.mta.ca; Tue, 13 Jun 2017 21:31:00 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9232 Archived-At: Dear Category Theorists, with my adviser Damiano Mazza and his other student Pierre Vial, we are = looking for a name =E2=80=93 or even better, a reference =E2=80=93 for the = following kind of functors: Let C and B be two categories, F : C ---> D a functor satisfying, for = all morphisms f:c -> c' in C: - if Ff =3D g \circ h, then there exists two morphisms k,l such that + f =3D k \circ l=20 + Fk =3D g + Fl =3D h - if Ff =3D id_a for a certain object a, then f itself is an identity. These functors arise when applying the Grothendieck construction to = relational presheaves: P : B ---> Rel. Indeed, the category of relational = presheaves on B is equivalent (through the Grothendieck construction) to a category = whose objects are such functors over B. If anyone could point us in a right direction, it would be much = appreciated. Best, =E2=80=94 Luc= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]