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Homotopy equivalences are equivalences: take 3
A basic fact in homotopy type theory is that homotopy equivalences are (coherent) equivalences. This is important because on the one hand, homotopy equivalences are the “correct” sort of equivalence,...
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The Simplex Category
I recently had occasion to define the simplex category inside of type theory. For some reason, I decided to use an inductive definition of each type of simplicial operators , rather than defining them...
View ArticleA Simpler Proof that π₁(S¹) is Z
Last year, Mike Shulman proved that π₁(S¹) is Z in Homotopy Type Theory. While trying to understand Mike’s proof, I came up with a simplification that shortens the proof a bunch (100 lines of Agda as...
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