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 $\infty$-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 \textit{ higher proof} (homotopy).
Categories: cs.LO