Theorems · Theorem · category theory
CochainComplex.HomComplex.Cochain.ofHoms_comp
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{F G K : CochainComplex C ℤ} (φ : (p : ℤ) → F.X p ⟶ G.X p) (ψ : (p : ℤ) → G.X p ⟶ K.X p),
(CochainComplex.HomComplex.Cochain.ofHoms φ).comp (CochainComplex.HomComplex.Cochain.ofHoms ψ) ⋯ =
CochainComplex.HomComplex.Cochain.ofHoms fun p => CategoryTheory.CategoryStruct.comp (φ p) (ψ p)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Preadditivestatement and proof · cited by 3,309
- add_zeroproof · cited by 2,707
- zero_addstatement and proof · cited by 2,366
- HomologicalComplex.Xstatement and proof · cited by 1,839
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cochainstatement · cited by 341
- CochainComplex.HomComplex.Cochain.compstatement and proof · cited by 115
- CochainComplex.HomComplex.Cochain.comp_zero_cochain_vproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.Cochain.ofHom_compproof · cited by 5