Theorems · Theorem · category theory
CochainComplex.mappingCocone.inl_v_snd_v_assoc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
{K L : CochainComplex C ℤ} (φ : K ⟶ L) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] (p q : ℤ) (hpq : p + -1 = q)
{Z : C} (h : L.X q ⟶ Z),
CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.inl φ).v p p ⋯)
(CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCocone.snd φ).v p q hpq) h) =
CategoryTheory.CategoryStruct.comp 0 h- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- add_zerostatement and proof · cited by 2,707
- HomologicalComplex.Xstatement and proof · cited by 1,839
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- CochainComplex.HomComplex.Cochain.vstatement and proof · cited by 213
- CochainComplex.mappingCoconestatement · cited by 46
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