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Prove associativity for natural transformations

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Frederik Hanghøj Iversen 2018-02-16 12:24:58 +01:00
parent b8994b8f4a
commit a64e2484e3
1 changed files with 11 additions and 2 deletions
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13
src/Cat/Categories/Fun.agda
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@ -9,6 +9,7 @@ import Cubical.GradLemma
module UIP = Cubical.GradLemma module UIP = Cubical.GradLemma
open import Cubical.Sigma open import Cubical.Sigma
open import Cubical.NType open import Cubical.NType
open import Cubical.NType.Properties
open import Data.Nat using (_≤_ ; z≤n ; s≤s) open import Data.Nat using (_≤_ ; z≤n ; s≤s)
module Nat = Data.Nat module Nat = Data.Nat
@ -125,10 +126,18 @@ module _ {ℓc ℓc' ℓd ℓd' : Level} {ℂ : Category ℓc ℓc'} {𝔻 : Cat
θ = proj₁ θ' θ = proj₁ θ'
η = proj₁ η' η = proj₁ η'
ζ = proj₁ ζ' ζ = proj₁ ζ'
θNat = proj₂ θ'
ηNat = proj₂ η'
ζNat = proj₂ ζ'
L : NaturalTransformation A D
L = (_:⊕:_ {A} {C} {D} ζ' (_:⊕:_ {A} {B} {C} η' θ'))
R : NaturalTransformation A D
R = (_:⊕:_ {A} {B} {D} (_:⊕:_ {B} {C} {D} ζ' η') θ')
_g⊕f_ = _:⊕:_ {A} {B} {C} _g⊕f_ = _:⊕:_ {A} {B} {C}
_h⊕g_ = _:⊕:_ {B} {C} {D} _h⊕g_ = _:⊕:_ {B} {C} {D}
:assoc: : (_:⊕:_ {A} {C} {D} ζ' (_:⊕:_ {A} {B} {C} η' θ')) ≡ (_:⊕:_ {A} {B} {D} (_:⊕:_ {B} {C} {D} ζ' η') θ') :assoc: : L ≡ R
:assoc: = Σ≡ (funExt (λ _ → assoc)) {!!} :assoc: = lemSig (naturalIsProp {F = A} {D})
L R (funExt (λ x → assoc))
where where
open IsCategory (isCategory 𝔻) open IsCategory (isCategory 𝔻)