Theorems · Theorem · category theory
CategoryTheory.ShortComplex.moduleCat_pOpcycles_eq_zero_iff
∀ {R : Type u} [inst : Ring R] (S : CategoryTheory.ShortComplex (ModuleCat R)) (x : ↑S.X₂),
(CategoryTheory.ConcreteCategory.hom S.pOpcycles) x = 0 ↔ x ∈ (ModuleCat.Hom.hom S.f).range- Cited by
- 0 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- map_zeroproof · cited by 1,614
- ModuleCatstatement and proof · cited by 1,429
- CategoryTheory.ShortComplex.X₂statement and proof · cited by 1,115
- ModuleCat.carrierstatement and proof · cited by 997
- sub_zeroproof · cited by 938
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.