From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6055 Path: news.gmane.org!not-for-mail From: soloviev@irit.fr Newsgroups: gmane.science.mathematics.categories Subject: Re: product for free Date: Wed, 18 Aug 2010 08:18:54 +0200 (CEST) Message-ID: References: Reply-To: soloviev@irit.fr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1282215829 6339 80.91.229.12 (19 Aug 2010 11:03:49 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 19 Aug 2010 11:03:49 +0000 (UTC) Cc: categories@mta.ca To: "David Leduc" Original-X-From: majordomo@mlist.mta.ca Thu Aug 19 13:03:47 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.138]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Om2uP-00081L-Bc for gsmc-categories@m.gmane.org; Thu, 19 Aug 2010 13:03:45 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:57055) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Om2tB-0002hy-59; Thu, 19 Aug 2010 08:02:29 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Om2t8-0008LA-4Y for categories-list@mlist.mta.ca; Thu, 19 Aug 2010 08:02:26 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6055 Archived-At: Remark: as far as I remember, one need to be cautios calling this a product, because ordinary product equations do not hold with this definition and standard equality of lambda-calculus. Best wishes Sergei Soloviev > Hi, > > In lambda-calculus one can define the product of types A and B by: > > forall C, (A->B->C)->C. > > with pairing and projections defined as: > > pair =E2=89=A1 =CE=BBx.=CE=BBy.=CE=BBz.z x y > fst =E2=89=A1 =CE=BBp.p (=CE=BBx.=CE=BBy.x) > snd =E2=89=A1 =CE=BBp.p (=CE=BBx.=CE=BBy.y) > > What would be the equivalent in a closed monoidal category? > Would we get a product for free? > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]