proposition: Lemma counit_is_epi_if_right_adjoint_is_faithful : faithful G -> ∏ x, isEpi (ε x).
proof: Proof. intros faithfulG. intros x y f g H. apply (Injectivity (# G)). apply incl_injectivity. - apply faithfulG. - apply (is_epi_post_whisker_right_adjoint_counit_pointwise x). apply (maponpaths #G) in H. do 2 rewrite functor_comp in H. assumption. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Epis UniMath.CategoryTheory.SplitMonicsAndEpis UniMath.CategoryTheory.Monics UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering