From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1090 Path: news.gmane.org!not-for-mail From: Tom KRANTZ Newsgroups: gmane.science.mathematics.categories Subject: On reflexivity Date: Sat, 20 Mar 1999 03:19:01 +0100 (MET) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017559 29452 80.91.229.2 (29 Apr 2009 15:05:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:05:59 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Sat Mar 20 10:22:39 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA17076 for categories-list; Sat, 20 Mar 1999 09:30:13 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:1090 Archived-At: A 'philosophical' interpretation of oriented graphs might be out of the scope of the categories mailing list, it seems elucidating to me though.(It could have been for Heraclit and Parmenides.) I suggest to consider vertices as states and edges as transitions. A reflexive edge corresponds to a transition from a state to itself. Two notions of morphism of oriented graphs come seem natural: - A rigid embedding which preserves difference of states - A notion of morphism which may equalize different states. The meaning of equality of states needs precision then. Coherence semantics deals with a different notion of graph. This is clear to me and can also be deduced from a discussion between Thomas Ehrhard and his student Pierre to which I assisted. This bears an answer to the question of reflexivity I think. Sincerely, Tom