Theorems · Theorem · category theory

CochainComplex.mappingCone.inl_fst

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G : CochainComplex C ℤ} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ],
  (CochainComplex.mappingCone.inl φ).comp ↑(CochainComplex.mappingCone.fst φ) ⋯ =
    CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.id F)

Defined in: Mathlib.Algebra.Homology.HomotopyCategory.MappingCone
Cited by: 2 results in Mathlib
Foundations: Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive HomologicalComplex.HasHomotopyCofiber

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Cites21

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.idstatement and proof · cited by 6,235
CategoryTheory.Preadditivestatement and proof · cited by 3,309
AddSubgroupstatement · cited by 3,232
HomologicalComplex.Xproof · cited by 1,839
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
CochainComplex.HomComplex.Cochainstatement and proof · cited by 341
neg_add_cancelstatement and proof · cited by 256
HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
CochainComplex.mappingConestatement and proof · cited by 181

Cited by2

Results whose statement or proof uses this declaration.

CochainComplex.mappingCone.inl_fst_assocproof · cited by 3
CochainComplex.mappingCone.liftCochain_fstproof · cited by 2