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Homotopy Type Theory: Univalent Foundations of Mathematics by The Univalent Foundations Program is a nonfiction available to read on EtoBox.

What is Homotopy Type Theory: Univalent Foundations of Mathematics about?

From the Introduction: 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 homotopy 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 brings new ideas into the very foundation of mathematics. On the one hand, there is Voevodsky’s subtle and beautiful univalence axiom. The univalence axiom implies, in particular, that isomorphic structures can be identified, a principle that mathematicians have been happily using on work- days, despite its incompatibility with the “official” doctrines of conventional foundations. On the other hand, we have higher inductive types, which provide direct, logical descriptions of some of the basic spaces and constructions of homotopy theory: spheres, cylinders, truncations, localizations, etc. Both ideas are impossible to capture directly in classical set-theoretic foundations, but when combined in homotopy type theory, they permit an entirely new kind of “logic of homotopy types”. This

Who reads Homotopy Type Theory: Univalent Foundations of Mathematics?

Author

The Univalent Foundations Program

Published

2013

Language

EN

Category

nonfiction

Subjects

Mathematics, Logic, Stem