Definition preserves_chosen_equalizer {C₁ C₂ : category} (HC₁ : Equalizers C₁) (F : C₁ ⟶ C₂) : UU := ∏ (x y : C₁) (f g : x --> y) (p : # F (EqualizerArrow (HC₁ x y f g)) · # F f = # F (EqualizerArrow (HC₁ x y f g)) · # F g), isEqualizer (#F f) (#F g) (#F (EqualizerArrow (HC₁ x y f g))) p.
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.