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The interpretation of intuitionistic type theory in locally cartesian closed categories: an intuitionistic approach

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I [Peter Dybjer] will give an intuitionistic view of Seely’s interpretation of Martin-Löf type in locally cartesian closed categories. The point is to use Martin-Löf type theory itself as metalanguage, and a constructive notion of category, a so called E-category. As a categorical substitute for the formal system of Martin-Löf type theory I will use E-categories with families, and discuss how to interpret such categories in E-locally cartesian closed categories. This is joint work with Alexandre Buisse, who has formalized the key part of this proof in Coq.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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