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@ -28,4 +28,8 @@
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}
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</style>
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<h1>HoTT Book Progress</h1>
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<h1>HoTT Book Progress</h1>
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<p>
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Last 7 days: <img src="https://wakapi.mzhang.io/api/badge/michael/interval:last_7_days/project:type-theory" />
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</p>
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@ -99,10 +99,27 @@ module theorem2∙1∙6 where
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Ω² {l} = Ω[_] {l = l} 2
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compose2 : {l : Level} {A : Set l} {a : A} → fst (Ω² (A , a)) → fst (Ω² (A , a)) → fst (Ω² (A , a))
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compose2 x y = x ∙ y
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compose2 x y = horiz x y
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where
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variable
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A : Set l
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a b c : A
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p q : a ≡ b
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r s : b ≡ c
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α : p ≡ q
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β : r ≡ s
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_∙ᵣ_ : p ≡ q → (r : b ≡ c) → p ∙ r ≡ q ∙ r
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α ∙ᵣ refl = sym (lemma2∙1∙4.i1 _) ∙ α ∙ lemma2∙1∙4.i1 _
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_∙ₗ_ : (q : a ≡ b) → r ≡ s → q ∙ r ≡ q ∙ s
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refl ∙ₗ β = sym (lemma2∙1∙4.i2 _) ∙ β ∙ lemma2∙1∙4.i2 _
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horiz : p ≡ q → r ≡ s → p ∙ r ≡ q ∙ s
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horiz α β = (α ∙ᵣ _) ∙ (_ ∙ₗ β)
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compose2-commutative : {l : Level} {A : Set l} {a : A} (x y : fst (Ω² (A , a))) → compose2 x y ≡ compose2 y x
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compose2-commutative {l} {A} {a} x y = {! !}
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compose2-commutative {l} {A} {a} x y = {! x !}
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```
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### Definition 2.1.7 (pointed type)
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