Linear Realisability and Cobordisms

Valentin Maestracci; Thomas Seiller

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arXiv · 2310.19339

Linear Realisability and Cobordisms

Valentin Maestracci·Thomas Seiller

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Abstract

Cobordism categories are known to be compact closed. They can therefore be used to define non-degenerate models of multiplicative linear logic by combining the Int construction with double glueing. In this work we detail such construction in the case of low-dimensional cobordisms, and exhibit a connexion between those models and the model of Interaction graphs introduced by Seiller. In particular, we exhibit how the so-called trefoil property is a consequence of the associativity of composition of higher structures, providing a first step toward establishing models as obtained from a double glueing construction. We discuss possible extensions to higher-dimensional cobordisms categories

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Valentin Maestracci, Thomas Seiller. 2023-10-30. Linear Realisability and Cobordisms. https://arxiv.org/abs/2310.19339

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