@@ -106,9 +106,9 @@ module _ {ℓC ℓC' ℓM ℓM' ℓA ℓA' : Level}
106106 path v = (F-hom Ran f) ⋆⟨ A ⟩ (F-hom Ran g) ⋆⟨ A ⟩ (limOut (limitA (z ↓Diag) (T* z)) v)
107107 ≡⟨ ⋆Assoc A _ _ _ ⟩
108108 (F-hom Ran f) ⋆⟨ A ⟩ ((F-hom Ran g) ⋆⟨ A ⟩ (limOut (limitA (z ↓Diag) (T* z)) v))
109- ≡⟨ cong (seq' A (F-hom Ran f)) (limArrowCommutes _ _ _ _) ⟩
109+ ≡⟨ cong (seq' A (F-hom Ran f)) (limArrowCommutes (limitA _ _) _ _ _) ⟩
110110 (F-hom Ran f) ⋆⟨ A ⟩ limOut (limitA (y ↓Diag) (T* y)) (j g .F-ob v)
111- ≡⟨ limArrowCommutes _ _ _ _ ⟩
111+ ≡⟨ limArrowCommutes (limitA _ _) _ _ _ ⟩
112112 limOut (limitA (x ↓Diag) (T* x)) (j f .F-ob (j g .F-ob v))
113113 ≡⟨ RanConeTrans f g v ⟩
114114 coneOut (RanCone (f ⋆⟨ C ⟩ g)) v ∎
@@ -121,7 +121,7 @@ module _ {ℓC ℓC' ℓM ℓM' ℓA ℓA' : Level}
121121 Ran .F-hom (K .F-hom f) ⋆⟨ A ⟩ coneOut (RanCone (id C)) (v , id C)
122122 ≡⟨ cong (λ g → Ran .F-hom (K .F-hom f) ⋆⟨ A ⟩ g) (sym (RanConeRefl (v , id C))) ⟩
123123 Ran .F-hom (K .F-hom f) ⋆⟨ A ⟩ limOut (limitA ((K .F-ob v) ↓Diag) (T* (K .F-ob v))) (v , id C)
124- ≡⟨ limArrowCommutes _ _ _ _ ⟩
124+ ≡⟨ limArrowCommutes (limitA _ _) _ _ _ ⟩
125125 coneOut (RanCone (K .F-hom f)) (v , id C)
126126 ≡⟨ cong (λ g → limOut (limitA ((K .F-ob u) ↓Diag) (T* (K .F-ob u))) (v , g))
127127 (⋆IdR C (K .F-hom f) ∙ sym (⋆IdL C (K .F-hom f))) ⟩
@@ -169,15 +169,15 @@ module _ {ℓC ℓC' ℓM ℓM' ℓA ℓA' : Level}
169169 (S .F-hom f ⋆⟨ A ⟩ N-ob σ y) ⋆⟨ A ⟩ limOut (limitA (y ↓Diag) (T* y)) (u , g)
170170 ≡⟨ ⋆Assoc A _ _ _ ⟩
171171 S .F-hom f ⋆⟨ A ⟩ (N-ob σ y ⋆⟨ A ⟩ limOut (limitA (y ↓Diag) (T* y)) (u , g))
172- ≡⟨ cong (seq' A (S .F-hom f)) (limArrowCommutes _ _ _ _) ⟩
172+ ≡⟨ cong (seq' A (S .F-hom f)) (limArrowCommutes (limitA _ _) _ _ _) ⟩
173173 S .F-hom f ⋆⟨ A ⟩ (S .F-hom g ⋆⟨ A ⟩ α .N-ob u)
174174 ≡⟨ sym (⋆Assoc A _ _ _) ⟩
175175 (S .F-hom f ⋆⟨ A ⟩ S .F-hom g) ⋆⟨ A ⟩ α .N-ob u
176176 ≡⟨ cong (λ h → h ⋆⟨ A ⟩ α .N-ob u) (sym (S .F-seq _ _)) ⟩
177177 S .F-hom (f ⋆⟨ C ⟩ g) ⋆⟨ A ⟩ α .N-ob u
178- ≡⟨ sym (limArrowCommutes _ _ _ _) ⟩
178+ ≡⟨ sym (limArrowCommutes (limitA _ _) _ _ _) ⟩
179179 N-ob σ x ⋆⟨ A ⟩ limOut (limitA (x ↓Diag) (T* x)) (u , f ⋆⟨ C ⟩ g)
180- ≡⟨ cong (seq' A (N-ob σ x)) (sym (limArrowCommutes _ _ _ _)) ⟩
180+ ≡⟨ cong (seq' A (N-ob σ x)) (sym (limArrowCommutes (limitA _ _) _ _ _)) ⟩
181181 N-ob σ x ⋆⟨ A ⟩ (Ran .F-hom f ⋆⟨ A ⟩ limOut (limitA (y ↓Diag) (T* y)) (u , g))
182182 ≡⟨ sym (⋆Assoc A _ _ _) ⟩
183183 (N-ob σ x ⋆⟨ A ⟩ Ran .F-hom f) ⋆⟨ A ⟩ limOut (limitA (y ↓Diag) (T* y)) (u , g) ∎
@@ -200,7 +200,7 @@ module _ {ℓC ℓC' ℓM ℓM' ℓA ℓA' : Level}
200200 S .F-hom (id C ⋆⟨ C ⟩ id C) ⋆⟨ A ⟩ α .N-ob u
201201 ≡⟨ refl ⟩
202202 NatTransCone S α (F-ob K u) .coneOut (u , id C ⋆⟨ C ⟩ id C)
203- ≡⟨ sym (limArrowCommutes _ _ _ _) ⟩
203+ ≡⟨ sym (limArrowCommutes (limitA _ _) _ _ _) ⟩
204204 limArrow (limitA ((K .F-ob u) ↓Diag) (T* (K .F-ob u))) _ (NatTransCone S α (F-ob K u))
205205 ⋆⟨ A ⟩ limOut (limitA ((K .F-ob u) ↓Diag) (T* (K .F-ob u))) (u , id C ⋆⟨ C ⟩ id C) ∎
206206
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