diff --git a/src/Cat/Categories/Fun.agda b/src/Cat/Categories/Fun.agda index de43087..70f75b7 100644 --- a/src/Cat/Categories/Fun.agda +++ b/src/Cat/Categories/Fun.agda @@ -45,9 +45,9 @@ module Fun {ℓc ℓc' ℓd ℓd' : Level} (ℂ : Category ℓc ℓc') (𝔻 : C (s≤s {n = Nat.suc Nat.zero} z≤n) (naturalIsProp θ) - module _ {A B C D : Functor ℂ 𝔻} {θ' : NaturalTransformation A B} - {η' : NaturalTransformation B C} {ζ' : NaturalTransformation C D} where - private + private + module _ {A B C D : Functor ℂ 𝔻} {θ' : NaturalTransformation A B} + {η' : NaturalTransformation B C} {ζ' : NaturalTransformation C D} where θ = proj₁ θ' η = proj₁ η' ζ = proj₁ ζ' @@ -58,11 +58,11 @@ module Fun {ℓc ℓc' ℓd ℓd' : Level} (ℂ : Category ℓc ℓc') (𝔻 : C L = (NT[_∘_] {A} {C} {D} ζ' (NT[_∘_] {A} {B} {C} η' θ')) R : NaturalTransformation A D R = (NT[_∘_] {A} {B} {D} (NT[_∘_] {B} {C} {D} ζ' η') θ') - _g⊕f_ = NT[_∘_] {A} {B} {C} - _h⊕g_ = NT[_∘_] {B} {C} {D} - :isAssociative: : L ≡ R - :isAssociative: = lemSig (naturalIsProp {F = A} {D}) - L R (funExt (λ x → 𝔻.isAssociative)) + _g⊕f_ = NT[_∘_] {A} {B} {C} + _h⊕g_ = NT[_∘_] {B} {C} {D} + isAssociative : L ≡ R + isAssociative = lemSig (naturalIsProp {F = A} {D}) + L R (funExt (λ x → 𝔻.isAssociative)) private module _ {A B : Functor ℂ 𝔻} {f : NaturalTransformation A B} where @@ -93,9 +93,9 @@ module Fun {ℓc ℓc' ℓd ℓd' : Level} (ℂ : Category ℓc ℓc') (𝔻 : C } instance - :isCategory: : IsCategory RawFun - :isCategory: = record - { isAssociative = λ {A B C D} → :isAssociative: {A} {B} {C} {D} + isCategory : IsCategory RawFun + isCategory = record + { isAssociative = λ {A B C D} → isAssociative {A} {B} {C} {D} ; isIdentity = λ {A B} → isIdentity {A} {B} ; arrowsAreSets = λ {F} {G} → naturalTransformationIsSets {F} {G} ; univalent = {!!} @@ -119,7 +119,7 @@ module _ {ℓ ℓ' : Level} (ℂ : Category ℓ ℓ') where } instance isCategory : IsCategory rawPresh - isCategory = Fun.:isCategory: _ _ + isCategory = Fun.isCategory _ _ Presh : Category (ℓ ⊔ lsuc ℓ') (ℓ ⊔ ℓ') Category.raw Presh = rawPresh