From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/625 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Challenge from Harvey Friedman Date: Thu, 29 Jan 1998 16:14:56 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017079 26566 80.91.229.2 (29 Apr 2009 14:57:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:57:59 +0000 (UTC) To: categories Original-X-From: cat-dist Thu Jan 29 16:16:54 1998 Original-Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id QAA32194; Thu, 29 Jan 1998 16:14:56 -0400 (AST) Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:625 Archived-At: Date: Wed, 28 Jan 1998 22:15:27 +0000 From: Carlos Simpson Being a newcomer to the category list, I have a really naive and stupid question (concerning H. Friedman's challenge). Namely, I was always under the impression that you had to know what a set was before you could talk about what a category was (in particular a topos). Is it possible to talk about toposes without knowing what a set is? This seems somewhat related to a question that has been bugging me for some time, namely how to talk about a ``category'' which is enhanced over itself, but not necessarily having any functor to or from Sets. The very first part of the structure would be a class of objects O together with a function (x,y)\mapsto H(x,y) from O\times O to O, but I can't get beyond that. ---Carlos Simpson