Homotopy Type Theory (paperback)

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Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between h omotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak °-groupoids. Homotopy type theory offers a new ÒunivalentÓ foundation of mathematics, in which a central role is played by VoevodskyÕs univalence axiom and higher inductive types. The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning Ñ but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant. We believe that univalent foundations will eventually become a viable alternative to set theory as the Òimplicit foundationÓ for the unformalized mathematics done by most mathematicians., mathematics, homotopy type theory, , Univalent Foundations Project| | 619PAGES Show more