From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1950 Path: news.gmane.org!not-for-mail From: Philippe Gaucher Newsgroups: gmane.science.mathematics.categories Subject: preprint : Investigating The Algebraic Structure of Dihomotopy Types Date: Mon, 7 May 2001 12:37:35 +0200 (MET DST) Message-ID: <200105071037.MAA21066@irmast2.u-strasbg.fr> Reply-To: Philippe Gaucher NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018226 1361 80.91.229.2 (29 Apr 2009 15:17:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:06 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon May 7 13:35:50 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f47FgxI20215 for categories-list; Mon, 7 May 2001 12:42:59 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Content-MD5: UD46CYDXyqWX9V/UPodX7w== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.3.5 SunOS 5.7 sun4u sparc Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 18 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:1950 Archived-At: Title : Investigating The Algebraic Structure of Dihomotopy Types Abstract : This presentation is the sequel of a paper published in GETCO'00 proceedings where a research program to construct an appropriate algebraic setting for the study of deformations of higher dimensional automata was sketched. This paper will be focused precisely on detailing some of its aspects. The main idea is that the category of homotopy types can be embedded in a new category of dihomotopy types, the embedding being realized by the Globe functor. In this latter category, isomorphism classes of objects are exactly higher dimensional automata up to deformations leaving invariant their computer scientific properties as presence or not of deadlocks (or everything similar or related). Some hints to study the algebraic structure of dihomotopy types are given, in particular a rule to decide whether a statement/notion concerning dihomotopy types is or not the lifting of another statement/notion concerning homotopy types. This rule does not enable to guess what is the lifting of a given notion/statement, it only enables to make the verification, once the lifting has been found. Comment : submitted to getco'01. expository paper. URL : http://www-irma.u-strasbg.fr/~gaucher/dihomotopy.ps.gz http://www-irma.u-strasbg.fr/~gaucher/dihomotopy.pdf