Theorems · Theorem · category theory

CategoryTheory.Abelian.LeftResolution.map_chainComplex_d_1_0_assoc

∀ {A : Type u_1} {C : Type u_2} [inst : CategoryTheory.Category.{v_1, u_2} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_1} A] {ι : CategoryTheory.Functor C A}
  (Λ : CategoryTheory.Abelian.LeftResolution ι) (X : A) [inst_2 : ι.Full] [inst_3 : ι.Faithful]
  [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C] [inst_5 : CategoryTheory.Abelian A] {Z : A}
  (h : ι.obj ((Λ.chainComplex X).X 0) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (ι.map ((Λ.chainComplex X).d 1 0)) h =
    CategoryTheory.CategoryStruct.comp (ι.map (Λ.chainComplexXOneIso X).hom)
      (CategoryTheory.CategoryStruct.comp (Λ.π.app (CategoryTheory.Limits.kernel (Λ.π.app X)))
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.kernel.ι (Λ.π.app X))
          (CategoryTheory.CategoryStruct.comp (ι.map (Λ.chainComplexXZeroIso X).inv) h)))

Defined in

Mathlib.Algebra.Homology.LeftResolution.Basic

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.FullCategoryTheory.Functor.FaithfulCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Abelian