From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9348 Path: news.gmane.org!.POSTED!not-for-mail From: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= Newsgroups: gmane.science.mathematics.categories Subject: Re: opposite category Date: Sat, 16 Sep 2017 15:44:32 +0000 Message-ID: References: , Reply-To: =?iso-8859-1?Q?Joyal=2C_Andr=E9?= NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1505693210 16820 195.159.176.226 (18 Sep 2017 00:06:50 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Mon, 18 Sep 2017 00:06:50 +0000 (UTC) To: Peter Selinger , Categories List Original-X-From: majordomo@mlist.mta.ca Mon Sep 18 02:06:44 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1dtjaE-00043T-54 for gsmc-categories@m.gmane.org; Mon, 18 Sep 2017 02:06:42 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:42249) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dtjbK-0002VW-HM; Sun, 17 Sep 2017 21:07:50 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dtjZM-0006Mc-0j for categories-list@mlist.mta.ca; Sun, 17 Sep 2017 21:05:48 -0300 Thread-Topic: categories: Re: opposite category Thread-Index: AQHTLkoQdUWH05xBjE+3zYxipuCCqaK3oMSH In-Reply-To: Accept-Language: en-US, en-CA Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9348 Archived-At: Dear Robert, Peter and all,=0A= =0A= We often turn covariant functors into contravariant ones:=0A= =0A= If C is a small category, then the category [C,Set]=0A= of covariant set valued functors on C is the topos of =0A= presheaves on C^{op}. =0A= =0A= Recall that the category \Gamma introduced by Graeme Segal =0A= is the opposite of the category Fin_\star of finite pointed sets.=0A= =0A= https://ncatlab.org/nlab/show/Segal%27s+category=0A= =0A= A Gamma-space was not defined by Segal to be a covariant functor=0A= Fin_\star --->Space but as a contravariant functor =0A= \Gamma---->Space =0A= =0A= https://ncatlab.org/nlab/show/Gamma-space=0A= =0A= -Andr=E9=0A= =0A= ________________________________________=0A= From: Peter Selinger [selinger@mathstat.dal.ca]=0A= Sent: Thursday, September 14, 2017 11:58 AM=0A= To: Categories List=0A= Subject: categories: Re: opposite category=0A= =0A= Robert Pare wrote:=0A= >=0A= > He said there may come a time when we have to consider covariant=0A= > functors as contravariant ones on the opposite category.=0A= =0A= This anecdote seems to have prompted a few posts about opposite=0A= categories, but I thought the point of the original anecdote was that=0A= Fred said that *covariant* functors should be considered as=0A= contravariant functors on the opposite category, i.e., that he=0A= considered contravariant functors to be the more fundamental concept.=0A= An interesting thought, and obviously tongue-in-cheek.=0A= =0A= -- Peter=0A= =0A= =0A= =0A= [For admin and other information see: http://www.mta.ca/~cat-dist/ ]