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The equivalence of the torus and the product of two circles in homotopy type theory (1510.03918v1)
Published 13 Oct 2015 in cs.LO and math.LO
Abstract: Homotopy type theory is a new branch of mathematics which merges insights from abstract homotopy theory and higher category theory with those of logic and type theory. It allows us to represent a variety of mathematical objects as basic type-theoretic constructions, higher inductive types. We present a proof that in homotopy type theory, the torus is equivalent to the product of two circles. This result indicates that the synthetic definition of torus as a higher inductive type is indeed correct.
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