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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| Vydáno v: | LICS 2016 : proceedings of the 31st annual ACM-IEEE Symposium on Logic in Computer Science : July 5-8, 2016, New York City, USA s. 565 - 574 |
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| Hlavní autoři: | , , , |
| Médium: | Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
New York, NY, USA
ACM
05.07.2016
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| Edice: | ACM Conferences |
| Témata: | |
| ISBN: | 9781450343916, 1450343910 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| ISBN: | 9781450343916 1450343910 |
| DOI: | 10.1145/2933575.2934545 |