Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.kernelSequenceCycles

{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) →
                  (n₀ n₁ : ℤ) →
                    autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.kernelSequenceCycles._auto_1 →
                      CategoryTheory.ShortComplex C

The short complex which expresses X.cycles as the kernel of X.δ.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian