Definition adj_equivalence_of_cats_inv : adj_equivalence_of_cats G. Proof. exists is_left_adjoint_inv. split; intro; unfold is_left_adjoint_inv; cbn. - apply (is_z_iso_inv_from_z_iso(_,,dirprod_pr2 (pr2 adEquivF) a)). - apply (is_z_iso_inv_from_z_iso(_,,dirprod_pr1 (pr2 adEquivF) b)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.PartA. 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.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.