Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.toCycles

{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) →
                  (fg : i ⟶ k) →
                    CategoryTheory.CategoryStruct.comp f g = fg →
                      (n : ℤ) → (X.H n).obj (CategoryTheory.ComposableArrows.mk₁ fg) ⟶ X.cycles f g n

The map H^n(fg) ⟶ H^n(g) factors through Z^n(f, g).

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

40 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian