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Higher inductive-recursive univalence and type-directed definitions
In chapter 2 of the HoTT book, we prove theorems (or, in a couple of cases, assert axioms) characterizing the equality types of all the standard type formers. For instance, we have and (that’s function...
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Fibrations with fiber an Eilenberg-MacLane space
One of the fundamental constructions of classical homotopy theory is the Postnikov tower of a space X. In homotopy type theory, this is just its tower of truncations: One thing that’s special about...
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