Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.liftCycles

{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) →
                  (n₀ n₁ : ℤ) →
                    (hn₁ : n₀ + 1 = n₁) →
                      {A : C} →
                        (x : A ⟶ (X.H n₀).obj (CategoryTheory.ComposableArrows.mk₁ g)) →
                          CategoryTheory.CategoryStruct.comp x (X.δ f g n₀ n₁ hn₁) = 0 → (A ⟶ X.cycles f g n₀)

Constructor for morphisms to X.cycles.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

4 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian