proposition: Lemma identity_functor_is_adj_equivalence {A : category} : adj_equivalence_of_cats (functor_identity A).
proof: Proof. use tpair. - exact is_left_adjoint_functor_identity. - now split; intros a; apply identity_is_z_iso. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core