proposition: Lemma are_adjoints_closed_under_iso_data {A B : category} (F G : functor A B) (H : functor B A) (αiso : @z_iso [A,B] F G) (HF : are_adjoints F H) : adjunction_data A B.
proof: Proof. set (α := pr1 αiso : nat_trans F G). set (αinv := inv_from_z_iso αiso : nat_trans G F). destruct HF as [[α' β'] [HF1 HF2]]. exists G. exists H. split. - apply (nat_trans_comp _ _ _ α' (post_whisker α H)). - apply (nat_trans_comp _ _ _ (pre_whisker H αinv) β'). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Epis UniMath.CategoryTheory.SplitMonicsAndEpis UniMath.CategoryTheory.Monics UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering