From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/274 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: question on finiteness in toposes Date: Sat, 11 Jan 1997 13:15:36 -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 1241016863 24994 80.91.229.2 (29 Apr 2009 14:54:23 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:23 +0000 (UTC) To: categories Original-X-From: cat-dist Sat Jan 11 13:15:55 1997 Original-Received: by mailserv.mta.ca; id AA05923; Sat, 11 Jan 1997 13:15:36 -0400 Original-Lines: 13 Xref: news.gmane.org gmane.science.mathematics.categories:274 Archived-At: Date: Sat, 11 Jan 1997 09:05:39 -0500 (EST) From: Peter Freyd Let me expand. If one bores into just why Set^2_kf can't be boolean and looks for a minimal example of its non-booleaness one inevitably lands on the object 2 -> 1. At first blush its lattice of subobjects does look boolean. Until one notices that there's a monomorphism from 2 -> 2 to 2 -> 1 (where 2 -> 2 is the identity map). Having noticed that, one has a quicker proof that it's not a topos: not every mono-epi is an equalizer.