One step closer to yoneda

This commit is contained in:
Frederik Hanghøj Iversen 2018-01-30 10:57:24 +01:00
parent eae441b659
commit 53816aeb74

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@ -58,35 +58,35 @@ module _ { : Level} { : Category } where
open Exponential
private
Cat = Cat
prshf = presheaf { = }
-- Exp : Set (lsuc (lsuc ))
-- Exp = Exponential (Cat (lsuc ) )
-- Sets (Opposite )
-- Exp : Set (lsuc (lsuc ))
-- Exp = Exponential (Cat (lsuc ) )
-- Sets (Opposite )
_⇑_ : (A B : Cat .Object) Cat .Object
A B = (exponent A B) .obj
where
open HasExponentials (Cat.hasExponentials )
_⇑_ : (A B : Cat .Object) Cat .Object
A B = (exponent A B) .obj
where
open HasExponentials (Cat.hasExponentials )
-- private
-- -- I need `Sets` to be a `Category ` but it simlpy isn't.
-- Setz : Category
-- Setz = {!Sets!}
-- :func*: : .Object (Setz Opposite ) .Object
-- :func*: A = {!!}
module _ {A B : .Object} (f : .Arrow A B) where
:func→: : NaturalTransformation (prshf A) (prshf B)
:func→: = (λ C x ( ._⊕_ f x)) , λ f₁ funExt λ x lem
where
lem = ( .isCategory) .IsCategory.assoc
module _ {c : .Object} where
eqTrans : (:func→: ( .𝟙 {c})) .proj₁ (Fun .𝟙 {o = prshf c}) .proj₁
eqTrans = funExt λ x funExt λ x .isCategory .IsCategory.ident .proj₂
eqNat : (i : I) Natural (prshf c) (prshf c) (eqTrans i)
eqNat i f = {!!}
-- prsh = presheaf { = }
-- k = prsh {!!}
-- :func*:' : .Object Presheaf
-- :func*:' = prsh
-- module _ {A B : .Object} (f : .Arrow A B) where
-- open import Cat.Categories.Fun
-- :func→:' : NaturalTransformation (prsh A) (prsh B)
:ident: : (:func→: ( .𝟙 {c})) (Fun .𝟙 {o = prshf c})
:ident: i = eqTrans i , eqNat i
yoneda : Functor (Fun { = Opposite } {𝔻 = Sets {}})
yoneda = record
{ func* = presheaf { = }
; func→ = {!!}
; ident = {!!}
{ func* = prshf
; func→ = :func→:
; ident = :ident:
; distrib = {!!}
}