Does Homotopy Type Theory Provide a Foundation for Mathematics?
نویسندگان
چکیده
منابع مشابه
Homotopy Type Theory: Univalent Foundations of Mathematics
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and beautiful"univalence axiom"implies that isomorphic structures can be identified. On the other hand,"higher inductive types"provide direct, logical descriptio...
متن کاملHomotopy Type Theory: Univalent Foundations of Mathematics
These lecture notes are based on and partly contain material from the HoTT book and are licensed under Creative Commons Attribution-ShareAlike 3.0.
متن کاملHomotopy type theory and the formalization of mathematics
er game, for mathematicians with an appreciation of detail. Finally, it gives peace of mind when ones arguments have been checked very carefully with the aid of a computer. Great formalization feats include: a formal proof of the Kepler conjecture [10], the four color theorem [8] and the Feit–Thompson theorem [9] (the beginning of the classification of finite simple groups). Notably, the former...
متن کاملHomotopy Type Theory
Introduction 3 1 A short guide to constructive type theory 7 1.1 A dependent type over a type . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 Dependent products . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.2 Dependent sums . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Defining types inductively . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Type theor...
متن کاملType Theory and Homotopy
The purpose of this informal survey article is to introduce the reader to a new and surprising connection between Geometry, Algebra, and Logic, which has recently come to light in the form of an interpretation of the constructive type theory of Per Martin-Löf into homotopy theory, resulting in new examples of certain algebraic structures which are important in topology. This connection was disc...
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ژورنال
عنوان ژورنال: The British Journal for the Philosophy of Science
سال: 2018
ISSN: 0007-0882,1464-3537
DOI: 10.1093/bjps/axw006