Cobordisms and commutative categorial grammars
arXiv:2107.08728
Abstract
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic proof-nets. We also introduce and study linear logic grammars, directly based on cobordisms and using classical multiplicative linear logic as a typing system.
This is the final version of the previously posted series of drafts on cobordimns and categorial grammars. Concise and, hopefully, much improved presentation, but no new mathematical content compared to preceding versions. arXiv admin note: text overlap with arXiv:1911.03962