Theorems · Theorem · category theory

CategoryTheory.ShortComplex.comp_pOpcycles_eq_zero_iff_up_to_refinements

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  {S : CategoryTheory.ShortComplex C} {A : C} (x₂ : A ⟶ S.X₂),
  CategoryTheory.CategoryStruct.comp x₂ S.pOpcycles = 0 ↔
    ∃ A' π,
      ∃ (_ : CategoryTheory.Epi π),
        ∃ x₁, CategoryTheory.CategoryStruct.comp π x₂ = CategoryTheory.CategoryStruct.comp x₁ S.f

Defined in

Mathlib.CategoryTheory.Abelian.Refinements

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian