From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6053 Path: news.gmane.org!not-for-mail From: David Leduc Newsgroups: gmane.science.mathematics.categories Subject: product for free Date: Tue, 17 Aug 2010 13:27:25 +0000 Message-ID: Reply-To: David Leduc 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 1282093439 11024 80.91.229.12 (18 Aug 2010 01:03:59 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 18 Aug 2010 01:03:59 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Aug 18 03:03:57 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OlX4K-0001QH-7U for gsmc-categories@m.gmane.org; Wed, 18 Aug 2010 03:03:52 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:43764) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OlX3L-0005SE-Hv; Tue, 17 Aug 2010 22:02:51 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OlX3J-0000O9-18 for categories-list@mlist.mta.ca; Tue, 17 Aug 2010 22:02:49 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6053 Archived-At: 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/ ]