Definition KATrivialDistinguished_TriMor (x : ob KAPreTriangData) (i' := @make_hfiber _ _ (# (ComplexHomotFunctor A)) _ _ (functor_id (ComplexHomotFunctor A) x)) : TriMor (TrivialTri x) (MappingConeTri (identity x) i'). Proof. use make_TriMor. - exact (make_MPMor (KATrivialDistinguished_MPMorMors x) (KATrivialDistinguished_MPMorsComm x)). - cbn. rewrite (@ZeroArrow_comp_left (ComplexHomot_Additive A)). rewrite (@ZeroArrow_comp_left (ComplexHomot_Additive A)). apply idpath. 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.NumberSystems.Integers. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. 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.Equivalences.Core. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.ShortExactSequences. Require Import UniMath.CategoryTheory.Categories.Abgr. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Morphisms. Require Import UniMath.CategoryTheory.AdditiveFunctors. Require Import UniMath.HomologicalAlgebra.Complexes. Require Import UniMath.HomologicalAlgebra.Triangulated. Require Import UniMath.HomologicalAlgebra.KA. Require Import UniMath.HomologicalAlgebra.TranslationFunctors. Require Import UniMath.HomologicalAlgebra.MappingCone.