_A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory_, LICS 2016 [[Kuen-Bang Hou (Favonia)]], [[Eric Finster]], [[Dan Licata]], [[Peter LeFanu Lumsdaine]] ## Abstract This paper continues investigations in "synthetic homotopy theory": the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory. We present a mechanized proof of the Blakers-Massey connectivity theorem, a result relating the higher-dimensional homotopy groups of a pushout type (roughly, a space constructed by gluing two spaces along a shared subspace) to those of the components of the pushout. This theorem gives important information about the pushout type, and has a number of useful corollaries, including the Freudenthal suspension theorem, which has been studied in previous formalizations. The new proof is more elementary than existing ones in abstract homotopy-theoretic settings, and the mechanization is concise and high-level, thanks to novel combinations of ideas from homotopy theory and type theory. ## Links * [arXiv:1605.03227](https://arxiv.org/abs/1605.03227) ## See also * [[Blakers-Massey Theorem]] * [[connectivity]] category: reference