Abstract
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).
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Martínez-Rivillas, D.O., de Queiroz, R.J.G.B. Towards a homotopy domain theory. Arch. Math. Logic 62, 559–579 (2023). https://doi.org/10.1007/s00153-022-00856-0
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DOI: https://doi.org/10.1007/s00153-022-00856-0