Free Compact 2-Categories

Abstract : Before one can attach a meaning to a sentence, one must distinguish different ways of parsing it. When analyzing 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 we describe its 2-cells as labeled 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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00137681
Contributor : Anne Preller <>
Submitted on : Tuesday, October 30, 2007 - 8:58:28 PM
Last modification on : Thursday, February 7, 2019 - 4:59:38 PM
Long-term archiving on: Friday, November 25, 2016 - 5:06:55 PM

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Anne Preller, Joachim Lambek. Free Compact 2-Categories. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2007, 17 (doi: 10.1017/S0960129506005901), pp.309-340. ⟨10.1017/S0960129506005901⟩. ⟨lirmm-00137681v2⟩

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