Theorems · Definition · category theory
CochainComplex.HomComplex.Cocycle.equivHom
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] →
(F G : CochainComplex C ℤ) → (F ⟶ G) ≃+ CochainComplex.HomComplex.Cocycle F G 0The additive equivalence between morphisms in CochainComplex C ℤ and 0-cocycles.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- ComplexShape.upstatement · cited by 1,123
- AddEquivstatement · cited by 1,087
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cocyclestatement · cited by 130
- CochainComplex.HomComplex.Cocycle.ofHomproof · cited by 23
- CochainComplex.HomComplex.Cocycle.homOfproof · cited by 9
- CochainComplex.HomComplex.Cocycle.ofHom_homOf_eq_selfproof · cited by 1
- CochainComplex.HomComplex.Cocycle.homOf_ofHom_eq_selfproof · cited by 0
Cited by7
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.Cocycle.equivHomShiftproof · cited by 23
- CochainComplex.homOfDegreewiseSplitproof · cited by 10
- CochainComplex.HomComplex.Cocycle.equivHomShift'proof · cited by 2
- CochainComplex.IsKInjective.eq_δ_of_cocycleproof · cited by 1
- CochainComplex.HomComplex.Cocycle.equivHom_applystatement and proof · cited by 0
- CochainComplex.HomComplex.Cocycle.equivHom_symm_applystatement and proof · cited by 0
- CochainComplex.HomComplex.Cochain.ofHom_injectiveproof · cited by 0