Theorems · Theorem · category theory
CochainComplex.HomComplex.Cochain.congr_v
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{F G : CochainComplex C ℤ} {n : ℤ} {z₁ z₂ : CochainComplex.HomComplex.Cochain F G n},
z₁ = z₂ → ∀ (p q : ℤ) (hpq : p + n = q), z₁.v p q hpq = z₂.v p q hpq- Cited by
- 11 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- HomologicalComplex.Xstatement · 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
- CochainComplex.HomComplex.Cochain.vstatement and proof · cited by 213
Cited by11
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.inl_v_descCochain_vproof · cited by 4
- CochainComplex.mappingCone.inr_f_descCochain_vproof · cited by 4
- CochainComplex.mappingCone.liftCochain_v_fst_vproof · cited by 3
- CochainComplex.mappingCone.liftCochain_v_snd_vproof · cited by 3
- CochainComplex.mappingCone.ext_cochain_from_iffproof · cited by 1
- CochainComplex.mappingCone.liftCochain_v_descCochain_vproof · cited by 1
- CochainComplex.HomComplex.Cocycle.fromSingleMk_surjectiveproof · cited by 1
- CochainComplex.mappingCone.id_Xproof · cited by 1
- CochainComplex.HomComplex.Cocycle.toSingleMk_surjectiveproof · cited by 1
- CochainComplex.Lifting.hasLiftproof · cited by 0
- CochainComplex.mappingCone.ext_cochain_to_iffproof · cited by 0