∀ {A : Type u_1} {A' : Type u_2} {B' : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} A]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} A'] [inst_2 : CategoryTheory.Category.{v_4, u_4} B'] {eA : A ≌ A'}
  {e' : A' ≌ B'} {F : CategoryTheory.Functor A B'} (hF : eA.functor.comp e'.functor ≅ F) (X : A),
  (AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso hF).hom.app X =
    CategoryTheory.CategoryStruct.comp (eA.unitIso.hom.app X)
      (CategoryTheory.CategoryStruct.comp (eA.inverse.map (e'.unitIso.hom.app (eA.functor.obj X)))
        (eA.inverse.map (e'.inverse.map (hF.hom.app X))))