Mathlib Map

Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.comp_neg

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G K : CochainComplex C ℤ} {n₁ n₂ n₁₂ : ℤ} (z₁ : CochainComplex.HomComplex.Cochain F G n₁)
  (z₂ : CochainComplex.HomComplex.Cochain G K n₂) (h : n₁ + n₂ = n₁₂), z₁.comp (-z₂) h = -z₁.comp z₂ h
Defined in
Mathlib.Algebra.Homology.HomotopyCategory.HomComplex
Cited by
1 results in Mathlib
Foundations
Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CochainComplex.mappingCone.δ_descCochain · cited by 1mappingCone.δ_descCochainCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCochainComplex · cited by 1016CochainComplexCochainComplex.HomComplex.Cochain · cited by 341HomComplex.CochainCochainComplex.HomComplex.Cochain.v · cited by 213Cochain.vCochainComplex.HomComplex.Cochain.comp · cited by 115Cochain.compCochainComplex.HomComplex.Cochain.ext · cited by 68Cochain.extCategoryTheory.Preadditive.comp_neg · cited by 32Preadditive.comp_negCochainComplex.HomComplex.Cochain.comp_v · cited by 30Cochain.comp_vCochain.comp_negCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.