Theorems · Theorem · category theory
CategoryTheory.ShortComplex.Exact.epi_f
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
{S : CategoryTheory.ShortComplex C}, S.Exact → S.g = 0 → CategoryTheory.Epi S.f- Cited by
- 8 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.X₂statement and proof · cited by 1,115
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.ShortComplex.X₁statement · cited by 889
- CategoryTheory.ShortComplex.X₃statement and proof · cited by 876
- CategoryTheory.Epistatement · cited by 688
- CategoryTheory.ShortComplex.gstatement and proof · cited by 658
- CategoryTheory.ShortComplex.fstatement and proof · cited by 653
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.Exact.epi_f_iffproof · cited by 2
- CategoryTheory.Abelian.SpectralObject.epi_H_map_twoδ₁Toδ₀proof · cited by 2
- CategoryTheory.ComposableArrows.Exact.isIso_map'proof · cited by 1
- CategoryTheory.ObjectProperty.isoModSerre_isInvertedBy_iffproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.isIso_map_fourδ₄Toδ₃proof · cited by 1
- ModuleCat.projectiveDimension_quotSMulTop_eq_succ_of_isSMulRegularproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.IsPresentable.injectivity₀.epi_fproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.isIso_fromOpcyclesproof · cited by 0