Do not export helpers in Fun
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@ -69,6 +69,7 @@ module Fun {ℓc ℓc' ℓd ℓd' : Level} (ℂ : Category ℓc ℓc') (𝔻 : C
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open RawCategory RawFun
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open Univalence (λ {A} {B} {f} → isIdentity {A} {B} {f})
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private
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module _ {A B : Functor ℂ 𝔻} where
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module A = Functor A
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module B = Functor B
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@ -328,6 +328,8 @@ module _ {ℓ : Level} where
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SetsHasProducts = record { product = product }
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module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
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open Category ℂ
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-- Covariant Presheaf
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Representable : Set (ℓa ⊔ lsuc ℓb)
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Representable = Functor ℂ (𝓢𝓮𝓽 ℓb)
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@ -336,8 +338,6 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
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Presheaf : Set (ℓa ⊔ lsuc ℓb)
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Presheaf = Functor (opposite ℂ) (𝓢𝓮𝓽 ℓb)
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open Category ℂ
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-- The "co-yoneda" embedding.
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representable : Category.Object ℂ → Representable
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representable A = record
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@ -28,9 +28,12 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
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private
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𝓢 = Sets ℓ
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open Fun (opposite ℂ) 𝓢
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presheaf = Cat.Categories.Sets.presheaf ℂ
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module ℂ = Category ℂ
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presheaf : ℂ.Object → Presheaf ℂ
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presheaf = Cat.Categories.Sets.presheaf ℂ
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module _ {A B : ℂ.Object} (f : ℂ [ A , B ]) where
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fmap : Transformation (presheaf A) (presheaf B)
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fmap C x = ℂ [ f ∘ x ]
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