From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6623 Path: news.gmane.org!not-for-mail From: claudio pisani Newsgroups: gmane.science.mathematics.categories Subject: question about monoidal categories Date: Mon, 18 Apr 2011 11:37:23 +0100 (BST) Message-ID: Reply-To: claudio pisani 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 1303174857 2881 80.91.229.12 (19 Apr 2011 01:00:57 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 19 Apr 2011 01:00:57 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Tue Apr 19 03:00:52 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QBzJD-0001OR-R9 for gsmc-categories@m.gmane.org; Tue, 19 Apr 2011 03:00:51 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:53859) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QBzJ9-00025T-2m; Mon, 18 Apr 2011 22:00:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QBzJ0-0000Gl-P2 for categories-list@mlist.mta.ca; Mon, 18 Apr 2011 22:00:39 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6623 Archived-At: Dear categorists,=0A=0Asuppose V is a monoidal category, with underlying ca= tegory V_0, and X is an ordinary category. Then (if I am not mistaken) the = functor category V_0^X has a monoidal structure, defined point-wise by that= of V and each functor f:X->Y gives a strong monoidal functor.=0A=0AFirst q= uestion : supposing V closed, under which hypothesis is V_0^X closed as wel= l (as in the case V =3D Set)?=0A=0ASecond question: supposing that V_0^X is= indeed closed and that V is suitably complete, so that reindexing along f = has a right adjoint forall_f, then V_0^X is enriched over V by forall_X(A->= B). How is this enrichment related to the usual one of [X,v] when X is a V= -category?=0A=0ABest regards,=0A=0AClaudio=0A=0A [For admin and other information see: http://www.mta.ca/~cat-dist/ ]