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Free compact 2-categories

Published online by Cambridge University Press:  01 April 2007

ANNE PRELLER  and
JOACHIM LAMBEK
ANNE PRELLER
Affiliation:
LIRMM/CNRS Montpellier, France Email: preller@lirmm.fr
JOACHIM LAMBEK
Affiliation:
McGill University Montréal, QC, Canada Email: lambek@math.mcgill.ca
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Before one can attach a meaning to a sentence, one must distinguish different ways of parsing it. When analysing a language with pregroup grammars, we are thus led to replace the free pregroup by a free compact strict monoidal category. Since a strict monoidal category is a 2-category with one 0-cell, we investigate the free compact 2-category generated by a given category, and describe its 2-cells as labelled transition systems. In particular, we obtain a decision procedure for the equality of 2-cells in the free compact 2-category.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 2 , April 2007 , pp. 309 - 340
Copyright
Copyright © Cambridge University Press 2007

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