* Paper on Feedback announced
@ 1998-02-28 16:41 Robert Seely
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From: Robert Seely @ 1998-02-28 16:41 UTC (permalink / raw)
To: Categories List, Types List; +Cc: Robin Cockett, Rick Blute
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 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
<rags@math.mcgill.ca>
<http://www.math.mcgill.ca>
[ NB - please use the "generic" email address above and not
machine specific e-addresses like "rags@triples.math.mcgill.ca" ]
===================================
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1998-02-28 16:41 Paper on Feedback announced Robert Seely
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