proposition: Lemma retract_functor_is_coequalizer {C D : category} (F : C ⟶ D) {a b : C} (H : retraction b a) : Coequalizer (#F (retraction_retraction H) · #F (retraction_section H)) (identity (F a)).
proof: Proof. exact (retract_is_coequalizer (functor_preserves_retraction F H)). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Univalence UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.LeftKanExtension UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Presheaf UniMath.CategoryTheory.Retracts UniMath.CategoryTheory.whiskering UniMath.AlgebraicTheories.FundamentalTheorem.SurjectivePrecomposition