An appropriate framework is put forward for the construction of $\lambda$-models with $\infty$-groupoid structure, which we call \textit{homotopic $\lambda$-models} through the use of an $\infty$-bicategory 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 \textit{higher proof} (homotopy).

翻译：提出了一个适当的框架,用于建造用美元或美元组别结构建造的$lambda美元模型,我们称之为\ textit{homotopic $\lambda$-models},通过使用一个有卡通卡片封闭和足够点的$infy$-bi类。我们据此开始一个概括Domain理论和$\lambda$-calulus的项目,意思是将美元和美元等价的证明概念(路径)提高到\ textit{higher proof}(homotoppy)。