Abstract
Homotopy type theory is an interpretation of constructive Martin-Lof type theory into abstract homotopy theory. It allows type theory to be used as a formal calculus for reasoning about homotopy theory, as well as more general mathematics such as can be formulated in category theory or set theory, under this new homotopical interpretation. Because constructive type theory has been implemented in computational proof assistants like Coq, it also facilitates the use of those tools in homotopy theory, category theory, set theory, and other fields of mathematics. This is the idea behind the new Univalent Foundations Program, which has recently been the object of quite intense investigation [4].
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