Theorems · Theorem · category theory

CochainComplex.mappingCone.inl_v_descShortComplex_f_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  (S : CategoryTheory.ShortComplex (CochainComplex C ℤ)) (i j : ℤ) (h : i + -1 = j) {Z : C} (h_1 : S.X₃.X j ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.inl S.f).v i j h)
      (CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.descShortComplex S).f j) h_1) =
    CategoryTheory.CategoryStruct.comp 0 h_1

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.ShortExact

Cited by

2 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian