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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... (Update)
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.... Has97b] Further discussions and applications of traced monoidal categories in the context of computer science are found in [Abr96, ABP98, BCS98]. As a precursor we note that Cazanescu and S tefanescu had the notion of biflows in mid 80s [CS88] whose axiomatization is...
.... ) tr U (f) ffl If f 2 I(U ) then f 2 I(U) and tr U (f) tr U (f) An alternative approach to partial traces is presented in [18], which considers traces on a linearly distributive category. The trace operator works on a certain subcategory, the core, which has the same...
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BibTeX entry: (Update)
Blute, R.F., Cockett, J.R.B., and Seely, R.A.G. (1998), Feedback for linearly distributive categories: traces and fixpoints, Manuscript. http://citeseer.ist.psu.edu/blute99feedback.html More
@misc{ blute98feedback,
author = "R. Blute and J. Cockett and R. Seely",
title = "Feedback for linearly distributive categories: traces and fixpoints",
year = "1998",
url = "citeseer.ist.psu.edu/blute99feedback.html" }
Citations (may not include all citations):69 Geometry of interaction I: Interpretation of system F (context) - Girard - 1989
50 New foundations for the geometry of interaction - Abramsky, Jagadeesan - 1994 ACM DBLP
43 Weakly distributive categories - Cockett, Seely - 1992
39 Retracing some paths (context) - Abramsky - 1996
38 Traced monoidal categories (context) - Joyal, Street et al. - 1996
37 Natural deduction and coherence for weakly distributive cate.. - Blute, Cockett et al. - 1996
36 The geometry of tensor calculus (context) - Joyal, Street - 1991
24 Geometry of Interaction II: Deadlock-Free Algorithms (context) - Girard - 1990
22 Lecture Notes in Mathematics (context) - Barr, Categories - 1979
18 Proof theory for full intuitionistic linear logic - Cockett, Seely - 1997
16 Annals of Pure and Applied Logic (context) - Blute, Scott et al. - 1996
11 Mathematical Structures in Computer Science (context) - Blute, Cockett et al. - 1996
8 Linearly distributive functors - Cockett, Seely - 1997
6 American Mathematical Society Colloquium Publications (context) - Algebraic - 1963
5 Nuclearity in the category of complete semilattices (context) - Higgs, Rowe - 1989
5 Models of sharing graphs (context) - Hasegawa - 1997 ACM
4 Duality of Vector Spaces (context) - Barr - 1976
2 A characterization of least-xed-point operator by dinaturali.. (context) - Simpson - 1993
2 Categorical combinators for charity - Vesely - 1997
1 Updated version available on http://www (context) - Cockett, Seely et al. - 1997
1 and Prakash Panangaden \Nuclear and trace ideals in tensored.. (context) - Abramsky, Blute - 1997
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