From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7366 Path: news.gmane.org!not-for-mail From: Ondrej Rypacek Newsgroups: gmane.science.mathematics.categories Subject: Alternative closed structure on Cat Date: Wed, 4 Jul 2012 15:10:37 +0100 Message-ID: Reply-To: Ondrej Rypacek NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (Apple Message framework v1278) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1341493748 26288 80.91.229.3 (5 Jul 2012 13:09:08 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 5 Jul 2012 13:09:08 +0000 (UTC) To: Categories List Original-X-From: majordomo@mlist.mta.ca Thu Jul 05 15:09:08 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Smlns-0003OW-Jg for gsmc-categories@m.gmane.org; Thu, 05 Jul 2012 15:09:05 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:53929) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Smln4-0002I0-7I; Thu, 05 Jul 2012 10:08:14 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Smln4-0000gq-2R for categories-list@mlist.mta.ca; Thu, 05 Jul 2012 10:08:14 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7366 Archived-At: Dear All Is there a name for and what is known about the tensor product of = ordinary categories which looks like the underlying 1-category of Gray's = (Gray) tensor product?=20 Explicitly, roughly:=20 - objects of C \otimes D are pairs (c,d) , c object of C , d an object = of D - arrows alternating lists of arrows from C and D, i.e. they are = generated by=20 (f,d) : (c,d) -> (c',d) for f : c -> c', (c,g) : (c,d) -> (c,d') for g : d -> d' and modulo the equations: (f',d) . (f, d) =3D (f'f, d), (c,g') . (c,g) = =3D (c,g'g), and identities, left and right unit laws and associativity = in each component separately. =09 And is the category of categories with respect to this tensor closed ?=20= Thank you! Ondrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]