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Over the past few years it has become apparent that there is a surprising and deep connection between constructive logic and higherdimensional structures in algebraic topology and category theory, in the form of an interpretation of the dependent type theory of Per Martin-Löf into classical homotopy theory. The interpretation results in a bridge between the worlds of constructive and classical mathematics which promises to shed new light on both. This mini-workshop brought together researchers in logic, topology, and cognate fields in order to explore both theoretical and practical ramifications of this discovery.
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Steve Awodey, Richard Garner, Per Martin-Löf, Vladimir Voevodsky, Mini-Workshop: The Homotopy Interpretation of Constructive Type Theory. Oberwolfach Rep. 8 (2011), no. 1, pp. 609–638DOI 10.4171/OWR/2011/11