Towards a Homotopy Domain Theory

Daniel O. Martínez-Rivillas, Ruy J. G. B. de Queiroz

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 of Kan complexes 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).

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