Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.cycles

{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] →
          CategoryTheory.Abelian.SpectralObject C ι → {i j k : ι} → (i ⟶ j) → (j ⟶ k) → ℤ → C

The kernel of δ : H^n(g) ⟶ H^{n+1}(f). In the documentation, this may be shortened as Z^n(f, g)

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

103 results in Mathlib

Foundations

Depth 63 from the axioms, rests on 1,227 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian