Towards a homotopy domain theory

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