

Homotopy Type Theory: Univalent Foundations of Mathematics [Book] - mazsa
http://homotopytypetheory.org/book/

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mazsa
"About the book

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 offers a new “univalent” foundation of mathematics, in which a central
role is played by Voevodsky’s 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 — 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
“implicit foundation” for the unformalized mathematics done by most
mathematicians."

The making of HoTT book [http://vimeo.com/68761218](http://vimeo.com/68761218)

