Theorems · Theorem · category theory
CategoryTheory.ComposableArrows.Exact.exact
∀ {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} (self : S.Exact) (i : ℕ)
(hi : autoParam (i + 2 ≤ n) CategoryTheory.ComposableArrows.Exact._auto_1), (S.sc ⋯ i hi).Exact- Defined in
- Mathlib.Algebra.Homology.ExactSequence
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.ShortComplex.Exactstatement · cited by 292
- CategoryTheory.ComposableArrows.Exactstatement and proof · cited by 65
- CategoryTheory.ComposableArrows.Exact.toIsComplexstatement · cited by 23
- CategoryTheory.ComposableArrows.scstatement · cited by 16
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.SpectralObject.exact₂proof · cited by 5
- CategoryTheory.ComposableArrows.exact₂_iffproof · cited by 4
- 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.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.natAddLEFunctor_obj_exactproof · cited by 3
- CategoryTheory.ComposableArrows.exact_of_isoproof · cited by 2
- CategoryTheory.Abelian.epi_of_mono_of_epi_of_mono'proof · cited by 2
- CategoryTheory.Abelian.mono_of_epi_of_epi_mono'proof · cited by 2