Theorems · Theorem · category theory

CategoryTheory.Triangulated.SpectralObject.Hom.comm_assoc

∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] [inst_2 : CategoryTheory.Limits.HasZeroObject C]
  [inst_3 : CategoryTheory.HasShift C ℤ] [inst_4 : CategoryTheory.Preadditive C]
  [inst_5 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_6 : CategoryTheory.Pretriangulated C]
  {X Y : CategoryTheory.Triangulated.SpectralObject C ι} (self : X.Hom Y) {i j k : ι} (f : i ⟶ j) (g : j ⟶ k) {Z : C}
  (h : (CategoryTheory.shiftFunctor C 1).obj (Y.ω₁.obj (CategoryTheory.ComposableArrows.mk₁ f)) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.δ f g)
      (CategoryTheory.CategoryStruct.comp
        ((CategoryTheory.shiftFunctor C 1).map (self.hom.app (CategoryTheory.ComposableArrows.mk₁ f))) h) =
    CategoryTheory.CategoryStruct.comp (self.hom.app (CategoryTheory.ComposableArrows.mk₁ g))
      (CategoryTheory.CategoryStruct.comp (Y.δ f g) h)

Defined in

Mathlib.CategoryTheory.Triangulated.SpectralObject

Cited by

0 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Pretriangulated