proposition: Lemma truth_about_ε (A: C'): ε A = φ_inv (identity (R A)).
proof: Proof. unfold φ_inv, φ_adj_inv. rewrite functor_id. apply pathsinv0. apply id_left. Qed.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Adjunctions.Core