Groupoids internal to assemblies on a partial combinatory algebra form a pi-tribe, hence a model of dependent type theory, with a model structure, W-types, a univalent impredicative universe, and 0-type homotopy category RT[A].
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A Model of Type Theory in Groupoid Assemblies
Groupoids internal to assemblies on a partial combinatory algebra form a pi-tribe, hence a model of dependent type theory, with a model structure, W-types, a univalent impredicative universe, and 0-type homotopy category RT[A].