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Abstract: Szabo's derivation systems on sequent calculi with exchange and product are not Church-Rosser. Thus his coherence results for categories having a symmetric product (either monoidal or cartesian) are false. 1 Introduction Gentzen's sequent calculi [9] have been applied extensively in category theory, e.g [2, 3, 4, 6, 7, 8]. Sequents correspond to morphisms of a category, and the rules of the calculus correspond to categorical structures (e.g. having an associative tensor product).... (Update)
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...was realized that its proofs contained flaws, and the Theorem published in [1] remained a conjecture. Furthermore, in a recent paper [7] C.B. Jay has shown that normalization result in chapter 8 is non correct. The detailed analysis of the proofs presented in chapters 7 and 8...
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2: Studies in Logic and the Foundations of Mathematics (context) - Szabo, Collected et al. - 1969
2: the conditions of full coherence in closed categories (context) - Soloviev - 1990
2: Topology and Logic as a Source of Algebra (context) - Lane - 1976
BibTeX entry: (Update)
C.B. Jay. Coherence in Category Theory and the Church-Rosser property. To appear in: Notre Dame Journal of Formal Logic, also accessible from the WWW-site: linus.socs.uts.edu.au/ cbj. http://citeseer.ist.psu.edu/jay93coherence.html More
@book{ jayjaycoherence,
author = "C. Barry Jay",
title = "Coherence in category theory and the Church-Rosser property",
volume = "ECS-LFCS-91-181 Notes: Includes bibliographical references Cover title",
publisher = "LFCS",
pages = "4p",
year = "Dept. of Computer Science",
url = "citeseer.ist.psu.edu/jay93coherence.html" }
Citations (may not include all citations):359 Introduction to higher order categorical logic (context) - Lambek, Scott - 1986
24 Coherence in closed categories (context) - Kelly, Lane - 1971
20 Studies in Logic and the Foundations of Mathematics (context) - Szabo, The et al. - 1969
8 Why commutative diagrams coincide with equivalent proofs (context) - Lane - 1982
7 Deductive systems and categories II. Standard constructions .. (context) - Lambek - 1969
6 The structure of free closed categories (context) - Jay - 1990
6 Algebra of Proofs (context) - Szabo - 1978
4 Coherence and non-commutative diagrams in closed categories (context) - Voreadou - 1977
3 Deductive systems and categories I. Syntactic calculus and r.. (context) - Lambek - 1968
2 A categorical equivalence of proofs (context) - Szabo - 1974
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