Definition preserves_reflexive_coequalizer {C₁ C₂ : category} (F : C₁ ⟶ C₂) : UU := ∏ (x y c : C₁) (f g : x --> y) (s : y --> x) (pf : s · f = identity _) (pg : s · g = identity _) (h : y --> c) (p : f · h = g · h) (Fp : #F f · #F h = #F g · #F h), isCoequalizer f g h p → isCoequalizer (#F f) (#F g) (#F h) Fp.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Adjunctions.Core.