Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.pOpcycles

{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) → (n : ℤ) → (X.H n).obj (CategoryTheory.ComposableArrows.mk₁ f) ⟶ X.opcycles f g n

The projection H^n(f) ⟶ opZ^n(f, g) to the cokernel of δ.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

43 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian