Theorems · Theorem · category theory
CategoryTheory.ComposableArrows.Exact.toIsComplex
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{n : ℕ} {S : CategoryTheory.ComposableArrows C n}, S.Exact → S.IsComplex- Defined in
- Mathlib.Algebra.Homology.ExactSequence
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.ComposableArrowsstatement and proof · cited by 627
- CategoryTheory.ComposableArrows.Exactstatement and proof · cited by 65
- CategoryTheory.ComposableArrows.IsComplexstatement · cited by 37
Cited by25
Results whose statement or proof uses this declaration.
- CategoryTheory.ComposableArrows.Exact.exactstatement · cited by 22
- CategoryTheory.Abelian.SpectralObject.zero₂proof · cited by 5
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_monoproof · cited by 3
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_mono'proof · cited by 3
- CategoryTheory.ComposableArrows.exact_iff_δlastproof · cited by 3
- CategoryTheory.ComposableArrows.exact_iff_δ₀proof · cited by 3
- CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_facproof · cited by 3
- CategoryTheory.Abelian.SpectralObject.zero₁proof · cited by 3
- CategoryTheory.Abelian.mono_of_epi_of_mono_of_monoproof · cited by 3
- CategoryTheory.Abelian.mono_of_epi_of_mono_of_mono'proof · cited by 3
- CategoryTheory.ComposableArrows.Exact.scproof · cited by 3
- CategoryTheory.ComposableArrows.natAddLEFunctor_obj_exactproof · cited by 3