Lemma IdentityIsQIS (C : (ComplexPreCat_AbelianPreCat A)) : isQIS (identity C). Proof. exact (pr2 (functor_on_iso (CohomologyFunctor A) (identity_iso C))). Qed.
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.