From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4472 Path: news.gmane.org!not-for-mail From: RONALD BROWN Newsgroups: gmane.science.mathematics.categories Subject: Re: Set as a monoidal category Date: Wed, 13 Aug 2008 09:36:36 +0000 (GMT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019968 13467 80.91.229.2 (29 Apr 2009 15:46:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:08 +0000 (UTC) To: Categories List Original-X-From: rrosebru@mta.ca Wed Aug 13 10:19:07 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 13 Aug 2008 10:19:07 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KTGFa-0001nZ-R3 for categories-list@mta.ca; Wed, 13 Aug 2008 10:18:54 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 7 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:4472 Archived-At: Dear Categoreans, =0A=0AIt is standard practice to answer a different quest= ion! But I can't resist referring to =0AR. Brown ``Ten topologies for $X\= times Y$'', {\em Quart. J.Math.}=0A(2) 14 (1963), 303-319.=0Aand asking if= one can modify these topologies or underlying sets by some process to work= sensibly for the category of sets? (a compact subset of a discrete space i= s of course finite). Maybe it is not possible. =0A=0ARonnie=0A=0A=0A=0A=0A= =0A=0A----- Original Message ----=0AFrom: Peter Selinger =0ATo: Categories List =0ASent: Wednesday, 13 Au= gust, 2008 1:23:59 AM=0ASubject: categories: Set as a monoidal category=0A= =0ADear Categoreans,=0A=0AI know three monoidal structures on the category = of sets, all of them=0Asymmetric. Two are the product and coproduct, and I'= ll leave it to=0Ayour imagination to figure out the third one.=0A=0AMy ques= tion is: are these the only three? Proofs, counterexamples, or=0Areferences= appreciated.=0A=0AThanks, -- Peter