Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.cyclesMap_i

∀ {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.Abelian C]
  (X : CategoryTheory.Abelian.SpectralObject C ι) {i j k : ι} (f : i ⟶ j) (g : j ⟶ k) {i' j' k' : ι} (f' : i' ⟶ j')
  (g' : j' ⟶ k') (α : CategoryTheory.ComposableArrows.mk₂ f g ⟶ CategoryTheory.ComposableArrows.mk₂ f' g')
  (β : CategoryTheory.ComposableArrows.mk₁ g ⟶ CategoryTheory.ComposableArrows.mk₁ g') (n : ℤ),
  autoParam (β = CategoryTheory.ComposableArrows.homMk₁ (α.app 1) (α.app 2) ⋯)
      CategoryTheory.Abelian.SpectralObject.cyclesMap_i._auto_1 →
    CategoryTheory.CategoryStruct.comp (X.cyclesMap f g f' g' α n) (X.iCycles f' g' n) =
      CategoryTheory.CategoryStruct.comp (X.iCycles f g n) ((X.H n).map β)

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

7 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian