Theorems · Theorem · category theory
CochainComplex.HomComplex.Cocycle.homOf_f
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{F G : CochainComplex C ℤ} (z : CochainComplex.HomComplex.Cocycle F G 0) (i : ℤ), z.homOf.f i = (↑z).v i i ⋯- Cited by
- 13 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- AddSubgroupstatement · cited by 3,232
- HomologicalComplex.Xstatement · cited by 1,839
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomologicalComplex.Hom.fstatement and proof · cited by 845
- CochainComplex.HomComplex.Cochainstatement · cited by 341
- CochainComplex.HomComplex.Cochain.vstatement · cited by 213
- CochainComplex.HomComplex.Cocyclestatement and proof · cited by 130
- CochainComplex.HomComplex.cocyclestatement · cited by 105
Cited by13
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.inr_f_desc_fproof · cited by 8
- CochainComplex.mappingCone.inl_v_desc_fproof · cited by 5
- CochainComplex.mappingCone.lift_f_snd_vproof · cited by 3
- CochainComplex.mappingCocone.lift_f_fst_fproof · cited by 2
- CochainComplex.mappingCone.lift_f_fst_vproof · cited by 2
- CochainComplex.HomComplex.Cocycle.ofHom_homOf_eq_selfproof · cited by 1
- CochainComplex.mappingCocone.lift_f_snd_vproof · cited by 1
- CochainComplex.mappingCocone.inl_v_desc_fproof · cited by 1
- CochainComplex.mappingCocone.inr_v_desc_fproof · cited by 1
- CochainComplex.mappingCone.lift_desc_fproof · cited by 1
- CochainComplex.mappingCocone.inr_v_fst_fproof · cited by 1
- CochainComplex.mappingCocone.id_Xproof · cited by 0