Theorems · Theorem · category theory

CategoryTheory.Functor.homologySequence_comp_assoc

∀ {C : Type u_1} {A : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  [inst_2 : CategoryTheory.Category.{v_3, u_3} A] (F : CategoryTheory.Functor C A)
  [inst_3 : CategoryTheory.Limits.HasZeroObject C] [inst_4 : CategoryTheory.Preadditive C]
  [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_6 : CategoryTheory.Pretriangulated C]
  [inst_7 : CategoryTheory.Abelian A] [F.IsHomological] [inst_9 : F.ShiftSequence ℤ],
  ∀ T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles,
    ∀ (n₀ : ℤ) {Z : A} (h : (F.shift n₀).obj T.obj₃ ⟶ Z),
      CategoryTheory.CategoryStruct.comp ((F.shift n₀).map T.mor₁)
          (CategoryTheory.CategoryStruct.comp ((F.shift n₀).map T.mor₂) h) =
        CategoryTheory.CategoryStruct.comp 0 h

Defined in

Mathlib.CategoryTheory.Triangulated.HomologicalFunctor

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.AbelianCategoryTheory.Functor.IsHomologicalCategoryTheory.Functor.ShiftSequence