Theorems · Theorem · category theory
CategoryTheory.ShortComplex.Exact.exact_toComposableArrows
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{S : CategoryTheory.ShortComplex C}, S.Exact → S.toComposableArrows.Exact- Defined in
- Mathlib.Algebra.Homology.ExactSequence
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.ShortComplex.Exactstatement and proof · cited by 292
- CategoryTheory.ShortComplex.zeroproof · cited by 76
- CategoryTheory.ComposableArrows.Exactstatement · cited by 65
- CategoryTheory.ShortComplex.toComposableArrowsstatement and proof · cited by 10
- CategoryTheory.ComposableArrows.exact₂_mkproof · cited by 7
Cited by20
Results whose statement or proof uses this declaration.
- HomologicalComplex.HomologySequence.composableArrows₅_exactproof · cited by 3
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_monoproof · cited by 3
- CategoryTheory.Abelian.mono_of_epi_of_mono_of_monoproof · cited by 3
- CategoryTheory.Abelian.SpectralObject.composableArrows₅_exactproof · cited by 2
- CategoryTheory.Abelian.epi_of_mono_of_epi_of_mono'proof · cited by 2
- CategoryTheory.Abelian.SpectralObject.sequenceΨ_exactproof · cited by 2
- CategoryTheory.Abelian.mono_of_epi_of_epi_mono'proof · cited by 2
- CategoryTheory.Abelian.Ext.contravariantSequence_exactproof · cited by 2
- HomologicalComplex.HomologySequence.composableArrows₂_exactproof · cited by 1
- CategoryTheory.Functor.homologySequenceComposableArrows₅_exactproof · cited by 1
- CategoryTheory.ShortComplex.epi_of_mono_of_epi_of_monoproof · cited by 1
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_epiproof · cited by 1