Theorems · Theorem · category theory

CategoryTheory.Triangulated.SpectralObject.comp_hom_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 Z : CategoryTheory.Triangulated.SpectralObject C ι} (α : X ⟶ Y) (β : Y ⟶ Z)
  {Z_1 : CategoryTheory.Functor (CategoryTheory.ComposableArrows ι 1) C} (h : Z.ω₁ ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp α β).hom h =
    CategoryTheory.CategoryStruct.comp α.hom (CategoryTheory.CategoryStruct.comp β.hom h)

Defined in

Mathlib.CategoryTheory.Triangulated.SpectralObject

Cited by

0 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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