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

翻译：已知协边范畴是紧闭范畴。因此，通过将Int构造与双重胶合相结合，它们可用于定义乘法线性逻辑的非退化模型。在此工作中，我们详细阐述了低维协边情况下的此类构造，并展示了这些模型与Seiller引入的交互图模型之间的联系。特别地，我们揭示了所谓的三叶结性质是更高结构复合结合性的结果，为建立由双重胶合构造所得的模型提供了第一步。我们还讨论了向更高维协边范畴扩展的可能性。