A Mechanization of the Blakers-Massey Connectivity Theorem in Homotopy Type Theory

• Published in: LICS 2016 : proceedings of the 31st annual ACM-IEEE Symposium on Logic in Computer Science : July 5-8, 2016, New York City, USA pp. 565 - 574
• Main Authors: Hou (Favonia), Kuen-Bang, Finster, Eric, Licata, Daniel R., Lumsdaine, Peter LeFanu
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 05.07.2016
• Series: ACM Conferences
• Subjects: matematisk logik; Mathematical Logic; Theory of computation; Theory of computation > Logic
• ISBN: 9781450343916; 1450343910
• DOI: 10.1145/2933575.2934545

This paper contributes to recent investigations of the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory. We present a mechanized proof of a result called the Blakers-Massey connectivity theorem, which relates the higher-dimensional loop structures of two spaces sharing a common part (represented by a pushout type, which is a generalization of a disjoint sum type) to those of the common part itself. This theorem gives important information about the pushout type, and has a number of useful corollaries, including the Freudenthal suspension theorem, which was used in previous formalizations. The proof is more direct than existing ones that apply in general category-theoretic settings for homotopy theory, and its mechanization is concise and high-level, due to novel combinations of ideas from homotopy theory and from type theory.