Parametricity of Extensionally Collapsed Term Models of Polymorphism and Their Categorical Properties

In the preceding paper, the author proved that parametric natural models have many categorical data types: finite products, finite coproducts, initial and terminal fixed points. In this paper, we show the second order minimum model is parametric, and thus enjoys the property. In addition to that, we give representation of internal right and left Kan extensions. We also show that extensionally collapsed models of closed types/terms collection are partially parametric, and that they have a part of the categorical data types above.

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