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arXiv · 1306.3703

Logical systems I: Lambda calculi through discreteness

Michal R. Przybylek
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Abstract

This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently (co)complete non-degenerate categories. As a simple corollary, we obtain a variant of Freyd theorem for categories internal to any tensored category. Also, with help of introduced concept of an associated category, we prove a representation theorem relating our internal models with well-studied fibrational models for polymorphism.

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BibTeXRIS

Michal R. Przybylek. 2014-10-15. Logical systems I: Lambda calculi through discreteness. https://arxiv.org/abs/1306.3703

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