From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8686 Path: news.gmane.org!not-for-mail From: Fabio Gadducci Newsgroups: gmane.science.mathematics.categories Subject: Re: categories of models of cartesian PROPs Date: Sun, 23 Aug 2015 16:09:35 +0200 Message-ID: References: Reply-To: Fabio Gadducci NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Mac OS X Mail 8.2 \(2102\)) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1440510013 32378 80.91.229.3 (25 Aug 2015 13:40:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 25 Aug 2015 13:40:13 +0000 (UTC) Cc: categories To: John Baez Original-X-From: majordomo@mlist.mta.ca Tue Aug 25 15:40:05 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.22]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1ZUES8-0005WB-TE for gsmc-categories@m.gmane.org; Tue, 25 Aug 2015 15:39:53 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44463) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ZUER7-0006nL-Tk; Tue, 25 Aug 2015 10:38:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ZUER8-0000sM-E7 for categories-list@mlist.mta.ca; Tue, 25 Aug 2015 10:38:50 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8686 Archived-At: Dear John, do not know if it may be useful, but you can say a few interesting = things wrt. models if each object of the prop T has just a co-monoid = structure (w/o being natural). In fact, you may e.g. capture partial = functions and relational algebras. Some details in Corradini-Gadducci, A functorial semantics for = multi-algebras and partial algebras. TCS 286(2): 293-322 (2002). Best, Fabio > On 22/ago/2015, at 03:49, John Baez wrote: >=20 > Hi - >=20 > I was reassured by a decategorified analogue: if T and C are = commutative >> monoids and we make the set of monoid homomorphism T -> C into a >> commutative monoid by pointwise multiplication, any one-variable = identity >> (like x^2 =3D x) obeyed by* either C or T* will be inherited by >> CommMon[T,C]. >>=20 >=20 > It seems that italicized text gets transmogrified here. I meant: >=20 > any one-variable identity (like x^2 =3D x) obeyed by either C or T = will be >> inherited by CommMon[T,C]. >>=20 >=20 > Best, > jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]