Definition equiv_Kernel1 {a b : C} (f : C⟦a, b⟧) (K : Limits.Kernels.Kernel (equiv_Zero2 Z) f) : Kernel f. Proof. use make_Equalizer. - exact K. - exact (KernelArrow K). - exact (equiv_Kernel1_eq f K). - exact (equiv_Kernel1_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.