Definition restricted_adjunction_counit : nat_trans (restricted_adjunction_right_adjoint ∙ restricted_adjunction_left_adjoint) (functor_identity (full_subcat_nat_trans_is_z_iso ε)). Proof. use make_nat_trans. - intro; cbn. use tpair. + apply ε. + exact tt. - intros ? ? ?. apply subtypePath; [intro; apply propproperty|]. apply (pr2 ε). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.Foundations.Propositions. 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.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering.