The Cayley-Dickson Construction in Homotopy Type Theory
  We define in the setting of homotopy type theory an H-space structure on $\mathbb S^3$. Hence we obtain a description of the quaternionic Hopf fibration $\mathbb S^3\hookrightarrow\mathbb S^7\twoheadrightarrow\mathbb S^4$, using only homotopy invariant tools. 
Ulrik Buchholtz and Egbert Rijke
math.AT cs.LO math.CT math.LO