Rename Opposite to opposite
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@ -108,7 +108,7 @@ module Fun {ℓc ℓc' ℓd ℓd' : Level} (ℂ : Category ℓc ℓc') (𝔻 : C
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module _ {ℓ ℓ' : Level} (ℂ : Category ℓ ℓ') where
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module _ {ℓ ℓ' : Level} (ℂ : Category ℓ ℓ') where
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open import Cat.Categories.Sets
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open import Cat.Categories.Sets
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open NaturalTransformation (Opposite ℂ) (𝓢𝓮𝓽 ℓ')
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open NaturalTransformation (opposite ℂ) (𝓢𝓮𝓽 ℓ')
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-- Restrict the functors to Presheafs.
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-- Restrict the functors to Presheafs.
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RawPresh : RawCategory (ℓ ⊔ lsuc ℓ') (ℓ ⊔ ℓ')
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RawPresh : RawCategory (ℓ ⊔ lsuc ℓ') (ℓ ⊔ ℓ')
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@ -88,7 +88,7 @@ module _ {ℓa ℓb : Level} where
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-- Contravariant Presheaf
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-- Contravariant Presheaf
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Presheaf : Set (ℓa ⊔ lsuc ℓb)
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Presheaf : Set (ℓa ⊔ lsuc ℓb)
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Presheaf = Functor (Opposite ℂ) (𝓢𝓮𝓽 ℓb)
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Presheaf = Functor (opposite ℂ) (𝓢𝓮𝓽 ℓb)
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-- The "co-yoneda" embedding.
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-- The "co-yoneda" embedding.
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representable : {ℂ : Category ℓa ℓb} → Category.Object ℂ → Representable ℂ
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representable : {ℂ : Category ℓa ℓb} → Category.Object ℂ → Representable ℂ
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@ -106,7 +106,7 @@ module _ {ℓa ℓb : Level} where
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open Category ℂ
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open Category ℂ
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-- Alternate name: `yoneda`
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-- Alternate name: `yoneda`
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presheaf : {ℂ : Category ℓa ℓb} → Category.Object (Opposite ℂ) → Presheaf ℂ
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presheaf : {ℂ : Category ℓa ℓb} → Category.Object (opposite ℂ) → Presheaf ℂ
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presheaf {ℂ = ℂ} B = record
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presheaf {ℂ = ℂ} B = record
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{ raw = record
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{ raw = record
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{ func* = λ A → ℂ [ A , B ] , arrowsAreSets
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{ func* = λ A → ℂ [ A , B ] , arrowsAreSets
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@ -336,4 +336,4 @@ module Opposite {ℓa ℓb : Level} where
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Category.raw (oppositeIsInvolution i) = rawInv i
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Category.raw (oppositeIsInvolution i) = rawInv i
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Category.isCategory (oppositeIsInvolution x) = {!!}
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Category.isCategory (oppositeIsInvolution x) = {!!}
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open Opposite public renaming (opposite to Opposite)
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open Opposite public
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@ -22,7 +22,7 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} (unprovable : IsCategory (RawCat
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open import Cat.Category.Exponential
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open import Cat.Category.Exponential
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open Functor
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open Functor
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𝓢 = Sets ℓ
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𝓢 = Sets ℓ
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open Fun (Opposite ℂ) 𝓢
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open Fun (opposite ℂ) 𝓢
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private
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private
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Catℓ : Category _ _
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Catℓ : Category _ _
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Catℓ = record { raw = RawCat ℓ ℓ ; isCategory = unprovable}
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Catℓ = record { raw = RawCat ℓ ℓ ; isCategory = unprovable}
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@ -22,7 +22,7 @@ module _ {ℓa ℓb : Level} where
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Substitutions = Arrow ℂ
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Substitutions = Arrow ℂ
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field
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field
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-- A functor T
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-- A functor T
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T : Functor (Opposite ℂ) (Fam ℓa ℓb)
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T : Functor (opposite ℂ) (Fam ℓa ℓb)
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-- Empty context
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-- Empty context
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[] : Terminal ℂ
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[] : Terminal ℂ
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private
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private
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