Definition restricted_adjunction_unit : nat_trans (functor_identity (full_subcat_nat_trans_is_z_iso η)) (restricted_adjunction_left_adjoint ∙ restricted_adjunction_right_adjoint). Proof. use make_nat_trans. - intro; cbn. use tpair. + apply η. + exact tt. - intros ? ? ?. apply subtypePath; [intro; apply propproperty|]. apply (pr2 η). 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.