Free compact 2-categories

Anne Preller (1) , Joachim Lambek

1 LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier

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.

Mots clés: compact 2-categories; non-symmetric monoidal categories; normalization; compact bilinear logic; categorial grammars; pregroup grammars

Domaines: Informatique et langage [cs.CL]; Catégories et ensembles [math.CT]

Anne Preller, Joachim Lambek. Free compact 2-categories. 12943, 2006, pp.26. ⟨lirmm-00117165⟩