30 lines
1.2 KiB
Agda
30 lines
1.2 KiB
Agda
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open import Level using (Level)
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-- open import Category.Core
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-- open import Relation.Binary.PropositionalEquality using (_≡_; refl)
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-- open import Data.Product using (_×_; Σ-syntax; _,_)
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-- open Category
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-- open Functor
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module Category.Instances.Cat {ℓ₁ ℓ₂ ℓ₃ : Level} where
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-- Cat : Category
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-- Cat .Obj = Category {ℓ₁} {ℓ₂} {ℓ₃}
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-- Cat .Hom 𝐂 𝐃 = Functor 𝐂 𝐃
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-- -- Cat ._≈_ {𝐂} {𝐃} 𝐅₁ 𝐅₂ = (∀ a → F₀ 𝐅₁ a ≡ F₀ 𝐅₂ a) × (∀ f → (_≈_ 𝐃) (F₁ 𝐅₁ f) {!!})
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-- Cat ._≈_ {𝐂} {𝐃} 𝐅₁ 𝐅₂ = Σ[ h ∈ (∀ a → F₀ 𝐅₁ a ≡ F₀ 𝐅₂ a) ]
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-- ∀ {a b : Obj 𝐂} → ∀ (f : Hom 𝐂 a b) → {!!}
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-- where
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-- transport : (a b : Obj 𝐂)
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-- → (F₀ 𝐅₁ a ≡ F₀ 𝐅₂ a)
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-- → (F₀ 𝐅₁ b ≡ F₀ 𝐅₂ b)
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-- → (Hom 𝐃 (F₀ 𝐅₁ a) (F₀ 𝐅₁ b))
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-- → (Hom 𝐃 (F₀ 𝐅₂ a) (F₀ 𝐅₂ b))
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-- transport a b h₁ h₂ H = {!!}
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-- Cat ._∘_ = {!!}
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-- Cat .𝟙 = {!!}
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-- Cat .assoc = {!!}
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-- Cat .identity-ˡ = {!!}
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-- Cat .identity-ʳ = {!!}
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-- Cat .equiv = {!!}
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-- Cat .≈-resp-∘ = {!!}
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