Theorems · Inductive type · category theory
CategoryTheory.ComposableArrows.Exact
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[CategoryTheory.Limits.HasZeroMorphisms C] → {n : ℕ} → CategoryTheory.ComposableArrows C n → PropF : ComposableArrows C n is exact if it is a complex and that all short
complexes consisting of two consecutive arrows are exact.
- Defined in
- Mathlib.Algebra.Homology.ExactSequence
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Limits.HasZeroMorphismsstatement · cited by 3,275
- CategoryTheory.ComposableArrowsstatement · cited by 627
Cited by78
Results whose statement or proof uses this declaration.
- CategoryTheory.ComposableArrows.Exact.toIsComplexstatement and proof · cited by 23
- CategoryTheory.ComposableArrows.Exact.exactstatement and proof · cited by 22
- CategoryTheory.ShortComplex.Exact.exact_toComposableArrowsstatement · cited by 20
- CategoryTheory.ComposableArrows.exact_of_δ₀statement and proof · cited by 10
- CategoryTheory.ComposableArrows.exact₂_mkstatement · cited by 7
- CategoryTheory.ComposableArrows.Exact.cokerIsoKer'statement and proof · cited by 6
- CategoryTheory.ComposableArrows.Exact.cokerToKer'statement and proof · cited by 6
- CategoryTheory.ComposableArrows.exact₂_iffstatement and proof · cited by 4
- CategoryTheory.Abelian.isIso_of_epi_of_isIso_of_isIso_of_monostatement and proof · cited by 4
- CategoryTheory.ComposableArrows.exact_iff_δlaststatement and proof · cited by 3
- CategoryTheory.ComposableArrows.exact_iff_δ₀statement and proof · cited by 3
- CategoryTheory.Abelian.epi_of_epi_of_epi_of_monostatement and proof · cited by 3