∀ {J : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} J] (F : CategoryTheory.Functor J MonCat) ⦃X Y : J⦄
  (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp (F.map f) (MonCat.Colimits.coconeMorphism F Y) =
    CategoryTheory.CategoryStruct.comp (MonCat.Colimits.coconeMorphism F X)
      (((CategoryTheory.Functor.const J).obj (MonCat.Colimits.colimit F)).map f)