Theorems · Theorem · category theory

CategoryTheory.SpectralSequence.comp_hom_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{u_3, u_1} C] [inst_1 : CategoryTheory.Abelian C] {κ : Type u_2}
  {c : ℤ → ComplexShape κ} {r₀ : ℤ} {X Y Z : CategoryTheory.SpectralSequence C c r₀} (f : X.Hom Y) (g : Y.Hom Z) (r : ℤ)
  (hr : r₀ ≤ r) {Z_1 : HomologicalComplex C (c r)} (h : Z.page r ⋯ ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.CategoryStruct.comp f g).hom r hr) h =
    CategoryTheory.CategoryStruct.comp (f.hom r ⋯) (CategoryTheory.CategoryStruct.comp (g.hom r ⋯) h)

Defined in

Mathlib.Algebra.Homology.SpectralSequence.Basic

Cited by

0 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian