Theorems · Theorem · category theory

CategoryTheory.SpectralSequence.Hom.comm

∀ {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} {E E' : CategoryTheory.SpectralSequence C c r₀} (self : E.Hom E') (r r' : ℤ)
  (pq : κ) (hrr' : autoParam (r + 1 = r') CategoryTheory.SpectralSequence.Hom._auto_5)
  (hr : autoParam (r₀ ≤ r) CategoryTheory.SpectralSequence.Hom._auto_7),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.homologyMap (self.hom r ⋯) pq) (E'.iso r r' pq ⋯ ⋯).hom =
    CategoryTheory.CategoryStruct.comp (E.iso r r' pq ⋯ ⋯).hom ((self.hom r' ⋯).f pq)

Defined in

Mathlib.Algebra.Homology.SpectralSequence.Basic

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian