Rename distrib to isDistributive

src/Cat/Categories/Cat.agda

@@ -107,13 +107,13 @@ module _ {ℓ ℓ' : Level} (unprovable : IsCategory (RawCat ℓ ℓ')) where
       proj₁ : Catt [ :product: , ℂ ]
       proj₁ = record
         { raw = record { func* = fst ; func→ = fst }
-        ; isFunctor = record { isIdentity = refl ; distrib = refl }
+        ; isFunctor = record { isIdentity = refl ; isDistributive = refl }
         }
 
       proj₂ : Catt [ :product: , 𝔻 ]
       proj₂ = record
         { raw = record { func* = snd ; func→ = snd }
-        ; isFunctor = record { isIdentity = refl ; distrib = refl }
+        ; isFunctor = record { isIdentity = refl ; isDistributive = refl }
         }
 
       module _ {X : Object Catt} (x₁ : Catt [ X , ℂ ]) (x₂ : Catt [ X , 𝔻 ]) where
@@ -125,7 +125,7 @@ module _ {ℓ ℓ' : Level} (unprovable : IsCategory (RawCat ℓ ℓ')) where
             }
           ; isFunctor = record
             { isIdentity   = Σ≡ x₁.isIdentity x₂.isIdentity
-            ; distrib = Σ≡ x₁.distrib x₂.distrib
+            ; isDistributive = Σ≡ x₁.isDistributive x₂.isDistributive
             }
           }
           where
@@ -279,14 +279,14 @@ module _ (ℓ : Level) (unprovable : IsCategory (RawCat ℓ ℓ)) where
             ηθ = proj₁ ηθNT
             ηθNat = proj₂ ηθNT
 
-          :distrib: :
+          :isDistributive: :
               𝔻 [ 𝔻 [ η C ∘ θ C ] ∘ func→ F ( ℂ [ g ∘ f ] ) ]
             ≡ 𝔻 [ 𝔻 [ η C ∘ func→ G g ] ∘ 𝔻 [ θ B ∘ func→ F f ] ]
-          :distrib: = begin
+          :isDistributive: = begin
             𝔻 [ (ηθ C) ∘ func→ F (ℂ [ g ∘ f ]) ]
               ≡⟨ ηθNat (ℂ [ g ∘ f ]) ⟩
             𝔻 [ func→ H (ℂ [ g ∘ f ]) ∘ (ηθ A) ]
-              ≡⟨ cong (λ φ → 𝔻 [ φ ∘ ηθ A ]) (H.distrib) ⟩
+              ≡⟨ cong (λ φ → 𝔻 [ φ ∘ ηθ A ]) (H.isDistributive) ⟩
             𝔻 [ 𝔻 [ func→ H g ∘ func→ H f ] ∘ (ηθ A) ]
               ≡⟨ sym isAssociative ⟩
             𝔻 [ func→ H g ∘ 𝔻 [ func→ H f ∘ ηθ A ] ]
@@ -314,7 +314,7 @@ module _ (ℓ : Level) (unprovable : IsCategory (RawCat ℓ ℓ)) where
           }
         ; isFunctor = record
           { isIdentity = λ {o} → :ident: {o}
-          ; distrib = λ {f u n k y} → :distrib: {f} {u} {n} {k} {y}
+          ; isDistributive = λ {f u n k y} → :isDistributive: {f} {u} {n} {k} {y}
           }
         }
 

src/Cat/Categories/Sets.agda

@@ -99,7 +99,7 @@ module _ {ℓa ℓb : Level} where
       }
     ; isFunctor = record
       { isIdentity = funExt λ _ → proj₂ isIdentity
-      ; distrib = funExt λ x → sym isAssociative
+      ; isDistributive = funExt λ x → sym isAssociative
       }
     }
     where
@@ -114,7 +114,7 @@ module _ {ℓa ℓb : Level} where
     }
     ; isFunctor = record
       { isIdentity = funExt λ x → proj₁ isIdentity
-      ; distrib = funExt λ x → isAssociative
+      ; isDistributive = funExt λ x → isAssociative
       }
     }
     where

src/Cat/Category/Functor.agda

@@ -34,7 +34,7 @@ module _ {ℓc ℓc' ℓd ℓd'}
     open RawFunctor F public
     field
       isIdentity : IsIdentity
-      distrib : IsDistributive
+      isDistributive : IsDistributive
 
   record Functor : Set (ℓc ⊔ ℓc' ⊔ ℓd ⊔ ℓd') where
     field
@@ -56,7 +56,7 @@ module _
   propIsFunctor : isProp (IsFunctor _ _ F)
   propIsFunctor isF0 isF1 i = record
     { isIdentity = 𝔻.arrowsAreSets _ _ isF0.isIdentity isF1.isIdentity i
-    ; distrib = 𝔻.arrowsAreSets _ _ isF0.distrib isF1.distrib i
+    ; isDistributive = 𝔻.arrowsAreSets _ _ isF0.isDistributive isF1.isDistributive i
     }
     where
       module isF0 = IsFunctor isF0
@@ -106,8 +106,8 @@ module _ {ℓ ℓ' : Level} {A B C : Category ℓ ℓ'} (F : Functor B C) (G : F
       dist : (F→ ∘ G→) (A [ α1 ∘ α0 ]) ≡ C [ (F→ ∘ G→) α1 ∘ (F→ ∘ G→) α0 ]
       dist = begin
         (F→ ∘ G→) (A [ α1 ∘ α0 ])         ≡⟨ refl ⟩
-        F→ (G→ (A [ α1 ∘ α0 ]))           ≡⟨ cong F→ (distrib G) ⟩
+        F→ (G→ (A [ α1 ∘ α0 ]))           ≡⟨ cong F→ (isDistributive G) ⟩
-        F→ (B [ G→ α1 ∘ G→ α0 ])          ≡⟨ distrib F ⟩
+        F→ (B [ G→ α1 ∘ G→ α0 ])          ≡⟨ isDistributive F ⟩
         C [ (F→ ∘ G→) α1 ∘ (F→ ∘ G→) α0 ] ∎
 
     _∘fr_ : RawFunctor A C
@@ -121,7 +121,7 @@ module _ {ℓ ℓ' : Level} {A B C : Category ℓ ℓ'} (F : Functor B C) (G : F
           F→ (G→ (𝟙 A))   ≡⟨ cong F→ (isIdentity G)⟩
           F→ (𝟙 B)        ≡⟨ isIdentity F ⟩
           𝟙 C             ∎
-        ; distrib = dist
+        ; isDistributive = dist
         }
 
   _∘f_ : Functor A C
@@ -136,6 +136,6 @@ identity = record
     }
   ; isFunctor = record
     { isIdentity = refl
-    ; distrib = refl
+    ; isDistributive = refl
     }
   }

src/Cat/Category/Properties.agda

@@ -88,6 +88,6 @@ module _ {ℓ : Level} {ℂ : Category ℓ ℓ} (unprovable : IsCategory (RawCat
       }
     ; isFunctor = record
       { isIdentity = :ident:
-      ; distrib = {!!}
+      ; isDistributive = {!!}
       }
     }