Definition monadic_repr_triangle_1 (HG : adj_equivalence_of_cats G) : adj_equivalence_of_cats F. Proof. use (two_out_of_three_comp _ _ _ is_monadic_commute_nat_z_iso). - exact HG. - exact comp_connecting_functor_equiv. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Properties.AdjunctionsRepresentable. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Monads.Examples.AdjunctionToMonad. Require Import UniMath.Bicategories.Monads.Examples.ToMonadInCat. Require Import UniMath.Bicategories.Monads.Examples.MonadsInBicatOfUnivCats. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.Limits.Examples.BicatOfUnivCatsLimits.