Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE

{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 l : ι} →
              (i ⟶ j) →
                (j ⟶ k) →
                  (k ⟶ l) →
                    (n₀ n₁ n₂ : ℤ) →
                      autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE._auto_1 →
                        autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE._auto_3 →
                          CategoryTheory.ShortComplex C

The (exact) sequence 0 ⟶ E^n(f₁, f₂, f₃) ⟶ opZ^n(f₂, f₃) ⟶ H^{n+1}(f₁).

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

13 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian