Definition CokernelKernelCohomology1_Mor2 (C : Complex (AbelianToAdditive A)) (i : hz) : A⟦(Kernel (pr1 (pr1 (CokernelKernelMorphism C i)))), (((CohomologyFunctor A C) : Complex (AbelianToAdditive A)) i)⟧. Proof. use (postcompose (CohomologyComplexIso_Mor_i A C i)). cbn. use KernelIn. - use (compose (KernelArrow _)). use CokernelOut. + exact (transportf (λ x' : A, precategory_morphisms x' _) (! maponpaths C (hzrminusplus i 1)) (CokernelArrow (Cokernel (transportf (precategory_morphisms (C (i - 1))) (maponpaths C (hzrminusplus i 1)) (Diff C (i - 1)))))). + exact (CokernelKernelCohomology1_eq C i). - exact (CokernelKernelCohomology1_Mor2_comm1 C i). Defined.
Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.BinDirectSums. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.AbelianToAdditive. Require Import UniMath.CategoryTheory.AdditiveFunctors. Require Import UniMath.HomologicalAlgebra.Complexes. Require Import UniMath.HomologicalAlgebra.KA.