An appropriate framework is put forward for the construction of \(\lambda \)-models with \(\infty \)-groupoid structure, which we call homotopic \(\lambda \)-models, through the use of an \(\infty \)-category with cartesian closure and enough points. With this, we establish the start of a project of generalization of Domain Theory and \(\lambda \)-calculus, in the sense that the concept of proof (path) of equality of \(\lambda \)-terms is raised to higher proof (homotopy).

中文翻译：

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迈向同伦域理论

通过使用\ ( \ _ _ _ _ _ infty \) - 具有笛卡尔闭包和足够点的类别。有了这个，我们建立了域理论和 \(\lambda \) -演算的泛化项目的开始，因为\(\lambda \ ) -terms 的相等性证明（路径）的概念被提升到更高的证明（同伦）。