From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/276 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: RE: question on finiteness in toposes Date: Sun, 12 Jan 1997 16:42:23 -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 1241016864 25000 80.91.229.2 (29 Apr 2009 14:54:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:54:24 +0000 (UTC) To: categories Original-X-From: cat-dist Sun Jan 12 16:43:17 1997 Original-Received: by mailserv.mta.ca; id AA18931; Sun, 12 Jan 1997 16:42:24 -0400 Original-Lines: 25 Xref: news.gmane.org gmane.science.mathematics.categories:276 Archived-At: Date: Sun, 12 Jan 97 01:31 EST From: Fred E J Linton <0004142427@mcimail.com> Supplementing Peter's answer to Streicher's K-finiteness question, I recall Prop. 7.4 on p. 97 of SLNM #753, which states, for presheaf topoi E = (C^op, Sets), that, with E_Kf the full subcategory of K-finite E-objects: E_Kf is balanced iff it's a topos iff each K-finite is decidable iff C is a "2-way" category iff ... . Streicher's >--> sure isn't 2-way, hence ... . The rest of that 20 year old report on my student Acun~a's thesis with me is also fun. -- Fred