This commit is contained in:
Michael Zhang 2023-08-05 05:58:45 -04:00
parent 6d0e500a59
commit 97a3ead49e
6 changed files with 31 additions and 14 deletions

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@ -1,5 +1,4 @@
2022 Oct 10
===
# 2022 Oct 10
```agda
{-# OPTIONS --cubical #-}

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@ -11,7 +11,7 @@ path-ind : {A : Set}
(C : (x y : A) x y Set)
(c : (x : A) C x x refl)
(x y : A) (p : x y) C x y p
path-ind C c x y p = ?
path-ind C c x y p = {! !}
-- Lemma 2.1.1
@ -52,13 +52,13 @@ ap f p i = f (p i)
lemma2111 : {A B : Set} (f : A B) (ie : isEquiv f) {a a : A}
isEquiv (ap f)
lemma2111 f ie .equiv-proof y = ?
lemma2111 f ie .equiv-proof y = {! !}
-- Lemma 2.11.2
lemma2112a : {A : Set} (a : A) {x₁ x₂ : A} (p : x₁ x₂) (q : a x₁)
transport ? p q p
lemma2112a a p q = ?
transport {! !} p q p
lemma2112a a p q = {! !}
-- Lemma 2.11.3

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@ -1,10 +1,11 @@
```
module HottBook.Chapter1 where
open import Relation.Binary.PropositionalEquality
open import Data.Empty
open import Data.Sum
Type = Set
open import HottBook.Common
```
## 1.7 Coproduct types
@ -21,3 +22,12 @@ A + B = A ⊎ B
¬_ : (A : Type) → Type
¬ A = A → ⊥
```
## 1.12.1 Path Induction
```
J : {A : Type} → (C : (x y : A) → x ≡ y → Type)
→ (c : (x : A) → C x x refl)
→ (x y : A) → (p : x ≡ y) → C x y p
J C c x x refl = c x
```

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@ -5,12 +5,14 @@ open import Relation.Binary.PropositionalEquality
open import Function
open import Data.Product
open import Data.Product.Properties
Type = Set
infixr 6 _∙_
_∙_ = trans
open import HottBook.Common
open import HottBook.Chapter1
```
> An internal error has occurred. Please report this as a bug.
> Location of the error: `__IMPOSSIBLE__`, called at src/full/Agda/Interaction/Imports.hs:915:15 in Agd-2.6.3-d4728884:Agda.Interaction.Imports
## 2.2 Functions are functors
### Lemma 2.2.1
@ -222,16 +224,16 @@ data 𝟙 : Set where
-- open import Function.HalfAdjointEquivalence
-- _is-⋆ : (x : 𝟙) → x ≡ ⋆
-- ⋆ is-⋆ = refl
--
--
-- theorem281-helper2 : {x : 𝟙} → (p : x ≡ x) → p ≡ refl
-- theorem281-helper2 {x} p =
-- theorem281-helper2 {x} p =
-- let a = sym (x is-⋆) ∙ p ∙ (x is-⋆) in
-- J (λ the what → p ≡ the) ? ?
--
--
-- theorem281-helper : {x y : 𝟙} → (p : x ≡ y) → (x is-⋆) ∙ sym (y is-⋆) ≡ p
-- theorem281-helper {x} p =
-- J (λ the what → (x is-⋆) ∙ sym (the is-⋆) ≡ what) p (theorem281-helper2 _)
--
--
-- theorem281 : (x y : 𝟙) → (x ≡ y) ≃ 𝟙
-- theorem281 x y = record
-- { to = λ _ → ⋆

6
src/HottBook/Common.agda Normal file
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@ -0,0 +1,6 @@
open import Relation.Binary.PropositionalEquality
Type = Set
infixr 6 _∙_
_∙_ = trans