From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8192 Path: news.gmane.org!not-for-mail From: Tom Hirschowitz Newsgroups: gmane.science.mathematics.categories,gmane.spam.detected Subject: generalised cartesian multicategories Date: Fri, 04 Jul 2014 16:34:44 +0200 Message-ID: <87lhs92nwb.fsf@hirscho.lama.univ-savoie.fr> Reply-To: Tom Hirschowitz NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1404540944 31288 80.91.229.3 (5 Jul 2014 06:15:44 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 5 Jul 2014 06:15:44 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Jul 05 08:15:37 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1X3JG4-0005Fv-RO for gsmc-categories@m.gmane.org; Sat, 05 Jul 2014 08:15:37 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46631) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1X3JFf-00056b-7G; Sat, 05 Jul 2014 03:15:11 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1X3JFf-0004bk-T2 for categories-list@mlist.mta.ca; Sat, 05 Jul 2014 03:15:11 -0300 User-Agent: Notmuch/0.18 (http://notmuchmail.org) Emacs/23.4.1 (x86_64-pc-linux-gnu) Precedence: bulk X-Spam-Report: 5.1 points; * -1.0 RCVD_IN_DNSWL_LOW RBL: Sender listed at http://www.dnswl.org/, low * trust * [138.73.1.186 listed in list.dnswl.org] * 1.8 DATE_IN_PAST_12_24 Date: is 12 to 24 hours before Received: date * 2.5 LOCALPART_IN_SUBJECT Local part of To: address appears in Subject * 1.8 MIME_QP_LONG_LINE RAW: Quoted-printable line longer than 76 chars Xref: news.gmane.org gmane.science.mathematics.categories:8192 gmane.spam.detected:5224548 Archived-At: Dear all, Cartesian multicategories are multicategories equipped with `contraction' and `weakening' operations. E.g., contraction associates to any morphism x=E2=82=81, =E2=80=A6, x=E2=82=99 =E2=86=92 y and 1 =E2=89= =A4 i =E2=89=A4 n such that x=E2=B1=BC =3D x_{j+1} for some j a morphism x=E2=82=81, =E2=80=A6, x=E2=B1=BC, x_{j+2}, =E2=80=A6 x= =E2=82=99 =E2=86=92 y. On the other hand we have generalised multicategories, which are monads in the bicategory of T-spans, for some cartesian monad T. I'm currently considering such a monad T for which cartesian multicategories make obvious sense, and wonder whether anyone has worked out a general setting for this. I.e., are there some known conditions on the monad T for cartesian T-multicategories to make sense? Of particular interest would be a setting in which free cartesian T-multcategories exist (over T-graphs). For those interested, the monad in question is on graphs. It's the composite of - the `free category' monad fc, and - the `free monoidal graph' monad fm, mapping any graph s,t : E =E2=86=92 = T to s*,t* : E* =E2=86=92 T*, made into a monad via the obvious distributive law fc =E2=88=98 fm =E2=86=92 fm =E2=88=98 fc. Any hints? Tom [For admin and other information see: http://www.mta.ca/~cat-dist/ ]