Theorems · Theorem · category theory

HomologicalComplex.alternatingConst_iCycles_even_comp_apply

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (A : C) {φ ψ : A ⟶ A} (hOdd : CategoryTheory.CategoryStruct.comp φ ψ = 0)
  (hEven : CategoryTheory.CategoryStruct.comp ψ φ = 0) {c : ComplexShape ℕ} [inst_2 : DecidableRel c.Rel]
  (hc : ∀ (i j : ℕ), c.Rel i j → Odd (i + j)) [inst_3 : CategoryTheory.CategoryWithHomology C] {j : ℕ},
  c.Rel (c.prev j) j →
    c.Rel j (c.next j) →
      Even j →
        ∀ {F : C → C → Type uF} {carrier : C → Type w}
          {instFunLike : (X Y : C) → FunLike (F X Y) (carrier X) (carrier Y)}
          [inst_4 : CategoryTheory.ConcreteCategory C F]
          (x : carrier ((HomologicalComplex.alternatingConst A hOdd hEven hc).cycles j)),
          (CategoryTheory.ConcreteCategory.hom φ)
              ((CategoryTheory.ConcreteCategory.hom ((HomologicalComplex.alternatingConst A hOdd hEven hc).iCycles j))
                x) =
            (CategoryTheory.ConcreteCategory.hom 0) x

Defined in

Mathlib.Algebra.Homology.AlternatingConst

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsDecidableRelCategoryTheory.CategoryWithHomologyCategoryTheory.ConcreteCategory