proposition: Lemma unique_adjoint_equivalence_comp {B : bicat} (HB : is_univalent_2 B) {a b c : B} : ∏ (f : adjoint_equivalence a b) (g : adjoint_equivalence b c), comp_adjequiv f g = comp_adjoint_equivalence (pr1 HB) a b c f g.
proof: Proof. use (J_2_0 (pr1 HB) (λ a b f, _)). intros x g; simpl. unfold comp_adjoint_equivalence. rewrite J_2_0_comp. use subtypePath. { intro. exact (isaprop_left_adjoint_equivalence _ (pr2 HB)). } cbn. apply (isotoid_2_1 (pr2 HB)). use make_invertible_2cell. - exact (lunitor (pr1 g)). - is_iso. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.BicategoryLaws UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Core.Univalence UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Morphisms.FullyFaithful UniMath.Bicategories.Morphisms.DiscreteMorphisms UniMath.Bicategories.Morphisms.InternalStreetFibration UniMath.Bicategories.Morphisms.InternalStreetOpFibration