Free compact 2-categories

@article{Preller2007FreeC2,
  title={Free compact 2-categories},
  author={Anne Preller and Joachim Lambek},
  journal={Mathematical Structures in Computer Science},
  year={2007},
  volume={17},
  pages={309 - 340}
}
  • A. Preller, J. Lambek
  • Published 1 April 2007
  • Computer Science, Mathematics
  • Mathematical Structures in Computer Science
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… 
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  • A. Preller
  • Computer Science, Mathematics
    J. Log. Lang. Inf.
  • 2007
Every pregroup grammar is shown to be strongly equivalent to one which uses basic types and left and right adjoints of basic types only. Therefore, a semantical interpretation is independent of the
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