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Groupoid Infinity

The Groupoid Infinity Cubical Base Library is compatible with hcomptrans branch of cubicaltt that fully supports recursive HITs. As example Hopf fibration is given formally due to Guillaume Brunerie:

rot: (x : S1) -> Path S1 x x = split
  base -> loop1
  loop @ i -> constSquare S1 base loop1 @ i

mu : S1 -> equiv S1 S1 = split
  base -> idEquiv S1
  loop @ i -> equivPath S1 S1 (idEquiv S1)
        (idEquiv S1) ( \(x : S1) -> rot x @ j) @ i

H : S2 -> U = split
  north -> S1
  south -> S1
  merid x @ i -> ua S1 S1 (mu x) @ i

total : U = (c : S2) * H c

Credits

  • Maxim Sokhatsky

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Hopf Fibrations Formalization

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