Lemma cancel_φ {A: C}{B: C'} (f g : L A --> B): φ f = φ g -> f = g. Proof. intro Hyp. apply (invmaponpathsweq (adjunction_hom_weq (pr2 is_left_adj_L) _ _)). exact Hyp. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.yoneda. Require Import UniMath.CategoryTheory.Adjunctions.Core.