Definition equiv_Kernel2 {a b : C} (f : C⟦a, b⟧) (K : Kernel f) : Limits.Kernels.Kernel (equiv_Zero2 Z) f. Proof. use make_Kernel. - exact (EqualizerObject C K). - exact (EqualizerArrow C K). - exact (equiv_Kernel2_eq f K). - exact (equiv_Kernel2_isEqualizer f K). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Zero. Require Import UniMath.CategoryTheory.Limits.Graphs.Equalizers. Require Import UniMath.CategoryTheory.Limits.Kernels.