diff --git a/Adjunction/Natural/Transformation/Universal.v b/Adjunction/Natural/Transformation/Universal.v index dedf46c2..6a1f7d4b 100644 --- a/Adjunction/Natural/Transformation/Universal.v +++ b/Adjunction/Natural/Transformation/Universal.v @@ -18,31 +18,29 @@ Context {U : C ⟶ D}. Program Definition Adjunction_from_Transform (A : F ∹ U) : F ⊣ U := {| adj := fun a b => - {| to := {| morphism := fun f => - fmap f ∘ @Transformation.unit _ _ _ _ A a |} - ; from := {| morphism := fun f => - @Transformation.counit _ _ _ _ A b ∘ fmap f |} |} + {| to := {| morphism := fun f =>n fmap f ∘ transform[unit[A]] a |} + ; from := {| morphism := fun f => transform[counit[A]] b ∘ fmap f |} |} |}. Next Obligation. proper; now rewrites. Qed. Next Obligation. proper; now rewrites. Qed. Next Obligation. rewrite fmap_comp. rewrite <- comp_assoc. - srewrite (naturality[@Transformation.unit _ _ _ _ A]). + srewrite (naturality[unit[A]]). rewrite comp_assoc. srewrite (@Transformation.fmap_counit_unit); cat. Qed. Next Obligation. rewrite fmap_comp. rewrite comp_assoc. - srewrite_r (naturality[@Transformation.counit _ _ _ _ A]). + srewrite_r (naturality[counit[A]]). rewrite <- comp_assoc. srewrite (@Transformation.counit_fmap_unit); cat. Qed. Next Obligation. rewrite fmap_comp. rewrite <- comp_assoc. - srewrite (naturality[@Transformation.unit _ _ _ _ A]). + srewrite (naturality[unit[A]]). now rewrite comp_assoc. Qed. Next Obligation. @@ -56,13 +54,13 @@ Qed. Next Obligation. rewrite fmap_comp. rewrite comp_assoc. - srewrite_r (naturality[@Transformation.counit _ _ _ _ A]). + srewrite_r (naturality[counit[A]]). now rewrite <- comp_assoc. Qed. Program Definition Adjunction_to_Transform {A : F ⊣ U} : F ∹ U := {| - Transformation.unit := {| transform := fun a => @unit _ _ _ _ A a |}; - Transformation.counit := {| transform := fun b => @counit _ _ _ _ A b |} + Transformation.unit := {| transform := fun _ => unit |}; + Transformation.counit := {| transform := fun _ => counit |} |}. Next Obligation. unfold unit.