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Fix typechecking
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valis committed Feb 21, 2024
1 parent cbb33d5 commit 5cd3179
Showing 1 changed file with 7 additions and 9 deletions.
16 changes: 7 additions & 9 deletions src/Homotopy/Localization/BlakersMassey.ard
Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,6 @@
\import HLevel
\import Homotopy.Fibration
\import Homotopy.Join
\import Homotopy.Localization.Accessible
\import Homotopy.Localization.Connected
\import Homotopy.Localization.Universe
\import Homotopy.Pushout
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\lemma surjective {d : Data} {x0 : X} {y0 : Y} (q : TruncP (\Sigma (y : Y) (Q x0 y))) : isConnectedMap (pbMap {d} {x0} {y0}) \elim q
| inP (y,q0) => \lam p => contr=>isConnected (Fib pbMap p) (DataExt.code-contr {\new DataExt { | Data => d | x0 => x0 | y0 => y | q0 => q0 }} p)

\class EquivData \noclassifying
(A B : \hType)
(M : A -> Connected) (N : B -> Connected)
(f : \Sigma (a : A) (M a) -> \Sigma (b : B) (N b))
(g : \Sigma (b : B) (N b) -> \Sigma (a : A) (M a))
(p : \Pi (a : A) (m : M a) -> (g (f (a,m))).1 = a)
(q : \Pi (b : B) (n : N b) -> (f (g (b,n))).1 = b)
\extends ReflUniverse {
\class EquivData \noclassifying (A B : \hType) \extends ReflUniverse {
| M : A -> Connected
| N : B -> Connected
| f : \Sigma (a : A) (M a) -> \Sigma (b : B) (N b)
| g : \Sigma (b : B) (N b) -> \Sigma (a : A) (M a)
| p : \Pi (a : A) (m : M a) -> (g (f (a,m))).1 = a
| q : \Pi (b : B) (n : N b) -> (f (g (b,n))).1 = b

\func eval (a : A) (m : M a) : lift (\lam a => sec {Connected.equiv {M a} (LType B)} (\lam m => lEta (f (a,m)).1)) (lEta a) = lEta (f (a,m)).1 =>
lift-prop (\lam a => sec {Connected.equiv {M a} (LType B)} (\lam m => lEta (f (a,m)).1)) a *> path (\lam i => (f_sec {Connected.equiv {M a} (LType B)} (\lam m => lEta (f (a,m)).1) @ i) m)
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