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Journal Articles Mathematical Structures in Computer Science Year : 2007

Free Compact 2-Categories

Joachim Lambek
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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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Dates and versions

lirmm-00137681 , version 1 (21-03-2007)
lirmm-00137681 , version 2 (30-10-2007)

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