proposition: Proposition pr1_category_form_adjunction : form_adjunction π terminal_functor terminal_functor_unit terminal_functor_counit.
proof: Proof. split. - intros x ; cbn. apply id_left. - intros x ; cbn. use total2_paths_f. + apply id_left. + use (TerminalArrowEq (T := terminal_in_fib T x)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation