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Abstract: Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions (only this case was considered in the original Mac Lane conjecture). Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered (together... (Update)
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BibTeX entry: (Update)
@misc{ soloviev-proof,
author = "Sergei Soloviev",
title = "Proof of a Conjecture of S. Mac Lane",
url = "citeseer.ist.psu.edu/soloviev96proof.html" }
Citations (may not include all citations):35 Linear logic and lazy computation (context) - Girard, Lafont - 1987
24 Coherence in Closed Categories (context) - Kelly, Lane - 1971
20 Studies in Logic and the Foundations of Mathematics (context) - Szabo, Proofs - 1978
17 Deductive Systems and Categories (context) - Lambek - 1968
17 The category of finite sets and cartesian closed categories (context) - Soloviev
13 Invariance and -definability (context) - Statman - 1982
6 The structure of free closed categories (context) - Jay - 1990
6 A generalization of the functorial calculus (context) - Eilenberg, Kelly - 1966
5 Closed categories and Proof Theory (context) - Mints - 1981
4 Coherence and non-commutative diagrams in closed categories (context) - Voreadou
2 with Appendix by Po-Hsuang Chu (context) - Barr, Categories - 1979
2 the conditions of full coherence in closed categories (context) - Soloviev - 1990
2 Lecture Notes in Math (context) - Lambek, Categories - 1969
2 Topology and Logic as a Source of Algebra (context) - Lane - 1976
2 Coherence in Category Theory and the Church-Rosser property - Jay
2 A cut-elimination theorem (context) - Kelly
1 Proceedings of the Conference on Categorical Algebra (context) - Eilenberg, Kelly
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