This commit is contained in:
Michael Zhang 2024-07-27 22:20:41 -05:00
parent 5d3ebb119b
commit e2212f7999
2 changed files with 24 additions and 3 deletions

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@ -28,4 +28,8 @@
}
</style>
<h1>HoTT Book Progress</h1>
<h1>HoTT Book Progress</h1>
<p>
Last 7 days: <img src="https://wakapi.mzhang.io/api/badge/michael/interval:last_7_days/project:type-theory" />
</p>

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@ -99,10 +99,27 @@ module theorem2∙1∙6 where
Ω² {l} = Ω[_] {l = l} 2
compose2 : {l : Level} {A : Set l} {a : A} → fst (Ω² (A , a)) → fst (Ω² (A , a)) → fst (Ω² (A , a))
compose2 x y = x ∙ y
compose2 x y = horiz x y
where
variable
A : Set l
a b c : A
p q : a ≡ b
r s : b ≡ c
α : p ≡ q
β : r ≡ s
_∙ᵣ_ : p ≡ q → (r : b ≡ c) → p ∙ r ≡ q ∙ r
α ∙ᵣ refl = sym (lemma2∙1∙4.i1 _) ∙ α ∙ lemma2∙1∙4.i1 _
_∙ₗ_ : (q : a ≡ b) → r ≡ s → q ∙ r ≡ q ∙ s
refl ∙ₗ β = sym (lemma2∙1∙4.i2 _) ∙ β ∙ lemma2∙1∙4.i2 _
horiz : p ≡ q → r ≡ s → p ∙ r ≡ q ∙ s
horiz α β = (α ∙ᵣ _) ∙ (_ ∙ₗ β)
compose2-commutative : {l : Level} {A : Set l} {a : A} (x y : fst (Ω² (A , a))) → compose2 x y ≡ compose2 y x
compose2-commutative {l} {A} {a} x y = {! !}
compose2-commutative {l} {A} {a} x y = {! x !}
```
### Definition 2.1.7 (pointed type)