Constructively Equivalent Propositions and Isomorphisms of Objects, or Terms as Natural Transformations
In these notes, we sketch a recent application of the typed and type-free λ-calculus to Proof Theory and Category Theory. The proof is fairly incomplete and we refer the reader interested in the lengthy technical details to Bruce & DiCosmo & Longo . Our main purpose here is to hint a logical framework for the result below, in a rather preliminary and problematic form. The occasion is provided by the kind invitation to deliver a lecture at a meeting with such a stimulating title.
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