proposition: Lemma are_adjoint_functor_cat_swap (C D : precategory) (E : category) : are_adjoints (@functor_cat_swap C D E) (@functor_cat_swap D C E).
proof: Proof. use tpair. - split; [ apply id_functor_cat_swap | apply functor_cat_swap_id ]. - apply form_adjunction_functor_cat_swap. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Adjunctions.Core