Theorems · Theorem · category theory
CategoryTheory.ShortComplex.exact_of_iso
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S₁ S₂ : CategoryTheory.ShortComplex C} (e : S₁ ≅ S₂), S₁.Exact → S₂.Exact- Cited by
- 18 results in Mathlib
- Foundations
- Depth 39 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
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Limits.IsZeroproof · cited by 306
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- CategoryTheory.ShortComplex.LeftHomologyData.Hproof · cited by 236
- CategoryTheory.ShortComplex.HomologyData.leftproof · cited by 130
- CategoryTheory.ShortComplex.HomologyDataproof · cited by 102
- CategoryTheory.ShortComplex.HomologyData.ofIsoproof · cited by 11
- CategoryTheory.ShortComplex.Exact.casesOnproof · cited by 5
Cited by18
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.homologySequence_exact₂proof · cited by 8
- CategoryTheory.Functor.homologySequence_exact₃proof · cited by 6
- CategoryTheory.ShortComplex.exact_iff_of_isoproof · cited by 6
- CategoryTheory.ShortComplex.ShortExact.homology_exact₂proof · cited by 6
- CategoryTheory.Functor.homologySequence_exact₁proof · cited by 5
- HomologicalComplex.ExactAt.of_isoproof · cited by 2
- CategoryTheory.ShortComplex.shortExact_of_isoproof · cited by 2
- CategoryTheory.ComposableArrows.exact_of_isoproof · cited by 2
- CategoryTheory.Functor.IsHomological.of_isoproof · cited by 1
- CategoryTheory.Functor.preservesMonomorphisms_of_map_exactproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesE_exactproof · cited by 1
- CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE_exactproof · cited by 1