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

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 t...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
ISBN:9781450343916
1450343910
DOI:10.1145/2933575.2934545