proposition: Lemma is_left_adjoint_functor_identity {A : category} : is_left_adjoint (functor_identity A).
proof: Proof. use tpair. + exact (functor_identity A). + exists (nat_trans_id _,, nat_trans_id _). abstract (now split; [intros a; apply id_left| intros a; apply id_left]). 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