From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/661 Path: news.gmane.org!not-for-mail From: Robert Seely Newsgroups: gmane.science.mathematics.categories Subject: Paper on Feedback announced Date: Sat, 28 Feb 1998 11:41:14 -0500 (EST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017105 26778 80.91.229.2 (29 Apr 2009 14:58:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:58:25 +0000 (UTC) Cc: Robin Cockett , Rick Blute To: Categories List , Types List Original-X-From: cat-dist Sat Feb 28 18:14:18 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id PAA27745 for categories-list; Sat, 28 Feb 1998 15:54:14 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-SMTP-Posting-Origin: Math.McGill.CA (Gauss.Math.McGill.CA [132.206.150.3]) Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 50 Xref: news.gmane.org gmane.science.mathematics.categories:661 Archived-At: The following paper is available on RAG Seely's WWW home page at or directly by ftp at or Comments are most welcome; please send them to any of the authors. Any problems in obtaining the paper should be sent to rags@math.mcgill.ca. Feedback for linearly distributive categories: traces and fixpoints by R.F. Blute J.R.B. Cockett R.A.G. Seely ABSTRACT In the present paper, we develop the notion of a trace operator on a linearly distributive category, which amounts to essentially working within a subcategory (the "core") which has the same sort of "type degeneracy" as a compact closed category. We also explore the possibility that an object may have several trace structures, introducing a notion of compatibility in this case. We show that if we restrict to compatible classes of trace operators, an object may have at most one trace structure (for a given tensor structure). We give a linearly distributive version of the "geometry of interaction" construction, and verify that we obtain a linearly distributive category in which traces become canonical. We explore the relationship between our notions of trace and fixpoint operators, and show that an object admits a fixpoint combinator precisely when it admits a trace and is a cocommutative comonoid. This generalises an observation of Hyland and Hasegawa. This paper is presented to Bill Lawvere on the occasion of his 60th birthday. =================================== RAG Seely [ NB - please use the "generic" email address above and not machine specific e-addresses like "rags@triples.math.mcgill.ca" ] ===================================