Subject: categories: Paper on Feedback announced

From: Robert Seely <[email-masked]>
Date: Sat, 28 Feb 1998 11:41:14 -0500 (EST)

The following paper is available on RAG Seely's WWW home page at
   <http://www.math.mcgill.ca/~rags>    or directly by ftp at
   <ftp://triples.math.mcgill.ca/pub/rags/linear/trace.ps.gz>
 or <ftp://triples.math.mcgill.ca/pub/rags/linear/trace.dvi.gz>

Comments are most welcome; please send them to any of the authors.
Any problems in obtaining the paper should be sent to [email-masked].

         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
<[email-masked]>
<http://www.math.mcgill.ca>

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