Comments in yoneda
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@ -56,8 +56,6 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
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open Exponential
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open Exponential
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private
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private
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Catℓ = Cat ℓ ℓ
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Catℓ = Cat ℓ ℓ
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CatHasExponentials : HasExponentials Catℓ
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CatHasExponentials = Cat.hasExponentials ℓ
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-- Exp : Set (lsuc (lsuc ℓ))
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-- Exp : Set (lsuc (lsuc ℓ))
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-- Exp = Exponential (Cat (lsuc ℓ) ℓ)
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-- Exp = Exponential (Cat (lsuc ℓ) ℓ)
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@ -66,7 +64,7 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
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_⇑_ : (A B : Catℓ .Object) → Catℓ .Object
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_⇑_ : (A B : Catℓ .Object) → Catℓ .Object
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A ⇑ B = (exponent A B) .obj
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A ⇑ B = (exponent A B) .obj
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where
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where
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open HasExponentials CatHasExponentials
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open HasExponentials (Cat.hasExponentials ℓ)
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private
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private
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-- I need `Sets` to be a `Category ℓ ℓ` but it simlpy isn't.
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-- I need `Sets` to be a `Category ℓ ℓ` but it simlpy isn't.
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@ -75,10 +73,17 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
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:func*: : ℂ .Object → (Setz ⇑ Opposite ℂ) .Object
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:func*: : ℂ .Object → (Setz ⇑ Opposite ℂ) .Object
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:func*: A = {!!}
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:func*: A = {!!}
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-- prsh = presheaf {ℂ = ℂ}
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-- :func*:' : ℂ .Object → Presheaf ℂ
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-- :func*:' = prsh
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-- module _ {A B : ℂ .Object} (f : ℂ .Arrow A B) where
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-- open import Cat.Categories.Fun
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-- :func→:' : NaturalTransformation (prsh A) (prsh B)
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yoneda : Functor ℂ (Setz ⇑ (Opposite ℂ))
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yoneda : Functor ℂ (Setz ⇑ (Opposite ℂ))
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yoneda = record
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yoneda = record
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{ func* = :func*:
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{ func* = :func*:
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; func→ = {!!}
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; func→ = {!:func→:'!}
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; ident = {!!}
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; ident = {!!}
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; distrib = {!!}
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; distrib = {!!}
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}
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}
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