Computer Science Department
School of Computer Science, Carnegie Mellon University


The Equivalence of the Torus and the Product
of Two Circles in Homotopy Type Theory

Kristina Sojakova

September 2015


Keywords: Homotopy type theory, torus, unit circle, higher inductive type

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.

23 pages

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