This commit is contained in:
Michael Zhang 2024-08-15 14:05:11 -05:00
parent 7ebaf615b0
commit 1c5a7e692e
3 changed files with 53 additions and 2 deletions

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@ -4,9 +4,11 @@ module CubicalHott.Chapter6 where
open import CubicalHott.Prelude
open import CubicalHott.Chapter3
open import Cubical.Data.Equality.Conversion
open import Cubical.HITs.Susp
open import Cubical.HITs.S1
open import Cubical.Data.Int
open import Cubical.Data.Nat
open import Cubical.Data.Bool
private
variable
@ -91,7 +93,6 @@ module lemma632 where
-- g : isSet Type
-- g x y p q = J (λ y' p' → (q' : x ≡ y') → p' ≡ q') goal p q
-- Corollary 6.10.13
module corollary61013 where

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@ -76,4 +76,19 @@ module section81 where
-- Lemma 8.1.8
encode-decode : (x : ) (c : code {l} x) encode {l} x (decode x c) c
encode-decode base c = {! !}
encode-decode (loop i) c = {! !}
encode-decode (loop i) c = {! !}
-- Definition 8.4.1
Type* = Σ Type (λ A A)
_→*_ : (A B : Type*) Type
_→*_ (A , a) (B , b) = Σ (A B) (λ f f a b)
-- Definition 8.4.2
Ω : Type* Type*
Ω (X , x) = (x x) , refl
Ωf : {X Y : Type*} (f : X * Y) Type* Type*
Ωf (f , f₀) p = {! sym f₀ ∙ ? !}

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@ -0,0 +1,35 @@
{-# OPTIONS --cubical #-}
module CubicalHott.Lemma651 where
open import CubicalHott.Prelude
open import CubicalHott.Chapter3
open import Cubical.HITs.Susp
open import Cubical.HITs.S1
open import Cubical.Data.Int
open import Cubical.Data.Nat
open import Cubical.Data.Bool
-- Lemma 6.5.1
module lemma651 where
lemma : Susp Bool
lemma = isoToEquiv (iso f g f-g g-f) where
f : Susp Bool
f north = base
f south = base
f (merid true i) = refl {x = base} i
f (merid false i) = loop i
g : Susp Bool
g base = north
g (loop i) = (merid false sym (merid true)) i
f-g : section f g
f-g base = refl
f-g (loop i) = {! !}
g-f : retract f g
g-f north = refl
g-f south = merid true
g-f (merid true i) = {! !}
g-f (merid false i) = {! !}