proposition: Proposition catiso_inv_mor_cat_iso {x₁ x₂ : C} (f : x₁ --> x₂) : catiso_inv_mor (#F f) = idtoiso (catiso_inv_ob_catiso x₁) · f · idtoiso (!(catiso_inv_ob_catiso x₂)).
proof: Proof. unfold catiso_inv_mor. rewrite !fully_faithful_inv_comp. rewrite fully_faithful_inv_hom_is_inv. rewrite !catiso_inv_hom_idtoiso. apply setcategory_eq_idtoiso_comp. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.UnivalenceAxiom UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful