From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6227 Path: news.gmane.org!not-for-mail From: Paul Levy Newsgroups: gmane.science.mathematics.categories Subject: Re: Freyd Categories Date: Sat, 25 Sep 2010 20:27:29 +0100 Message-ID: References: Reply-To: Paul Levy NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v936) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1285451918 16537 80.91.229.12 (25 Sep 2010 21:58:38 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 25 Sep 2010 21:58:38 +0000 (UTC) Cc: categories To: David Leduc Original-X-From: majordomo@mlist.mta.ca Sat Sep 25 23:58:36 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 1OzclP-0003AC-Sq for gsmc-categories@m.gmane.org; Sat, 25 Sep 2010 23:58:36 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:58454) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OzckY-0005CC-KS; Sat, 25 Sep 2010 18:57:42 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OzckT-0000aR-CL for categories-list@mlist.mta.ca; Sat, 25 Sep 2010 18:57:37 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6227 Archived-At: On 23 Sep 2010, at 12:01, David Leduc wrote: > A Freyd category is essentially a functor. That's right. It's neither a category nor due to Freyd. > So why is it called a category?! I think there were two reasons. Firstly to portray the category of computations as being more important than the category of values. Secondly because an identity-on-objects functor between two categories with the same objects can be regarded as an [ -> , Set ] enriched category. Here -> is the category with two objects and a morphism between them (and identities). This point is emphasized in John Power's paper "Premonoidal categories as categories with algebraic structure" in TCS in 2002. Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 (0)121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]