Theorems · Theorem · category theory
ModuleCat.shortComplex_exact
∀ {R : Type u} [inst : Ring R] (S : CategoryTheory.ShortComplex (ModuleCat R)),
Function.Exact ⇑(CategoryTheory.ConcreteCategory.hom S.f) ⇑(CategoryTheory.ConcreteCategory.hom S.g) → S.Exact- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 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.
Cites16
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
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- ModuleCatstatement and proof · cited by 1,429
- CategoryTheory.ShortComplex.X₂statement · cited by 1,115
- ModuleCat.carrierstatement · cited by 997
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.X₃statement · cited by 876
- CategoryTheory.ShortComplex.gstatement and proof · cited by 658
Cited by2
Results whose statement or proof uses this declaration.
- ModuleCat.smulShortComplex_exactproof · cited by 1
- ModuleCat.shortComplexOfConj_exactproof · cited by 0