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

Use omap/fmap

Browse source
This commit is contained in:
Frederik Hanghøj Iversen 2018-03-06 09:56:44 +01:00
parent bdd67aee53
commit 9173468b03
1 changed files with 8 additions and 13 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

19
src/Cat/Category/Monad.agda
View file

@ -22,8 +22,6 @@ module Monoidal {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
open NaturalTransformation ℂ ℂ open NaturalTransformation ℂ ℂ
record RawMonad : Set ℓ where record RawMonad : Set ℓ where
field field
-- TODO rename fields here
-- R ~ m
R : EndoFunctor ℂ R : EndoFunctor ℂ
pureNT : NaturalTransformation F.identity R pureNT : NaturalTransformation F.identity R
joinNT : NaturalTransformation F[ R ∘ R ] R joinNT : NaturalTransformation F[ R ∘ R ] R
@ -40,9 +38,6 @@ module Monoidal {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
joinN : Natural F[ R ∘ R ] R joinT joinN : Natural F[ R ∘ R ] R joinT
joinN = proj₂ joinNT joinN = proj₂ joinNT
private
module R = Functor R
Romap = Functor.func* R Romap = Functor.func* R
Rfmap = Functor.func→ R Rfmap = Functor.func→ R
@ -51,15 +46,15 @@ module Monoidal {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
IsAssociative : Set _ IsAssociative : Set _
IsAssociative = {X : Object} IsAssociative = {X : Object}
→ joinT X ∘ R.func→ (joinT X) ≡ joinT X ∘ joinT (R.func* X) → joinT X ∘ Rfmap (joinT X) ≡ joinT X ∘ joinT (Romap X)
IsInverse : Set _ IsInverse : Set _
IsInverse = {X : Object} IsInverse = {X : Object}
→ joinT X ∘ pureT (R.func* X) ≡ 𝟙 → joinT X ∘ pureT (Romap X) ≡ 𝟙
× joinT X ∘ R.func→ (pureT X) ≡ 𝟙 × joinT X ∘ Rfmap (pureT X) ≡ 𝟙
IsNatural = ∀ {X Y} f → joinT Y ∘ R.func→ f ∘ pureT X ≡ f IsNatural = ∀ {X Y} f → joinT Y ∘ Rfmap f ∘ pureT X ≡ f
IsDistributive = ∀ {X Y Z} (g : Arrow Y (R.func* Z)) (f : Arrow X (R.func* Y)) IsDistributive = ∀ {X Y Z} (g : Arrow Y (Romap Z)) (f : Arrow X (Romap Y))
→ joinT Z ∘ R.func→ g ∘ (joinT Y ∘ R.func→ f) → joinT Z ∘ Rfmap g ∘ (joinT Y ∘ Rfmap f)
≡ joinT Z ∘ R.func→ (joinT Z ∘ R.func→ g ∘ f) ≡ joinT Z ∘ Rfmap (joinT Z ∘ Rfmap g ∘ f)
record IsMonad (raw : RawMonad) : Set ℓ where record IsMonad (raw : RawMonad) : Set ℓ where
open RawMonad raw public open RawMonad raw public