fredefox/cat
1
0
Fork 0
Code Issues Pull requests Releases Wiki Activity

used presheaf as first component of yoneda

Browse source
This commit is contained in:
Andrea Vezzosi 2018-01-25 17:04:00 +00:00
parent ee2e84edfe
commit 2295022619
1 changed files with 10 additions and 8 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

18
src/Cat/Category/Properties.agda
View file

@ -52,6 +52,8 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
open import Cat.Category open import Cat.Category
open Category open Category
open import Cat.Categories.Cat using (Cat) open import Cat.Categories.Cat using (Cat)
open import Cat.Categories.Fun
open import Cat.Categories.Sets
module Cat = Cat.Categories.Cat module Cat = Cat.Categories.Cat
open Exponential open Exponential
private private
@ -66,12 +68,12 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
where where
open HasExponentials (Cat.hasExponentials ℓ) open HasExponentials (Cat.hasExponentials ℓ)
private -- private
-- I need `Sets` to be a `Category ℓ ℓ` but it simlpy isn't. -- -- I need `Sets` to be a `Category ℓ ℓ` but it simlpy isn't.
Setz : Category ℓ ℓ -- Setz : Category ℓ ℓ
Setz = {!Sets!} -- Setz = {!Sets!}
:func*: : ℂ .Object → (Setz ⇑ Opposite ℂ) .Object -- :func*: : ℂ .Object → (Setz ⇑ Opposite ℂ) .Object
:func*: A = {!!} -- :func*: A = {!!}
-- prsh = presheaf {ℂ = ℂ} -- prsh = presheaf {ℂ = ℂ}
-- k = prsh {!!} -- k = prsh {!!}
@ -81,9 +83,9 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} where
-- open import Cat.Categories.Fun -- open import Cat.Categories.Fun
-- :func→:' : NaturalTransformation (prsh A) (prsh B) -- :func→:' : NaturalTransformation (prsh A) (prsh B)
yoneda : Functor ℂ (Setz ⇑ (Opposite ℂ)) yoneda : Functor ℂ (Fun {ℂ = Opposite ℂ} {𝔻 = Sets {ℓ}})
yoneda = record yoneda = record
{ func* = :func*: { func* = presheaf {ℂ = ℂ}
; func→ = {!!} ; func→ = {!!}
; ident = {!!} ; ident = {!!}
; distrib = {!!} ; distrib = {!!}