From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1962 Path: news.gmane.org!not-for-mail From: Newsgroups: gmane.science.mathematics.categories Subject: preprint: Ordered PCA's and Realizability Toposes Date: Tue, 15 May 2001 13:08:08 +0200 (MET DST) Message-ID: <200105151108.NAA15073@kodder.math.uu.nl> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018234 1420 80.91.229.2 (29 Apr 2009 15:17:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:14 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed May 16 22:37:59 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f4H1AD313125 for categories-list; Wed, 16 May 2001 22:10:13 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sun-Charset: US-ASCII Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 30 Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:1962 Archived-At: Paper available: P.J.W. Hofstra and J. van Oosten, Ordered PCA's and Realizability Toposes http://www.math.uu.nl/people/jvoosten/papers.html Abstract: The concept of Ordered PCA (Partial Combinatory Algebra) is defined; it is a generalization of ordinary PCA's. The construction of Realizability Toposes for OPCA's is straightforward. Two 2-categories OPCA and OPCA+ are defined, OPCA+ being a lluf subcategory of OPCA. Both have a 2-monad I on them. It is shown that the category of realizability triposes over opca's with Set-indexed exact functors is equivalent to the Kleisli category of I on OPCA, whereas the category of realizabiloity triposes with geometric morphisms is the Kleisli category for I on OPCA+. This extends and analyzes results in the theses of Pitts and Longley. As an application we obtain an elegant tripos presentation of Menni's chain of toposes, constructed as exact completions.