Theorems · Inductive type · category theory
CategoryTheory.ComposableArrows.IsComplex
{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 a complex if all compositions of
two consecutive arrows are zero.
- Defined in
- Mathlib.Algebra.Homology.ExactSequence
- Cited by
- 37 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 by50
Results whose statement or proof uses this declaration.
- CategoryTheory.ComposableArrows.Exact.toIsComplexstatement · cited by 23
- CategoryTheory.ComposableArrows.scstatement and proof · cited by 16
- CategoryTheory.ComposableArrows.IsComplex.zerostatement and proof · cited by 16
- CategoryTheory.ComposableArrows.sc'statement and proof · cited by 7
- CategoryTheory.ComposableArrows.sc'Mapstatement and proof · cited by 5
- CategoryTheory.ComposableArrows.scMapstatement and proof · cited by 5
- CategoryTheory.ComposableArrows.IsComplex.cokerToKer'statement and proof · cited by 5
- CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_facstatement and proof · cited by 5
- CategoryTheory.ComposableArrows.exact₂_iffstatement and proof · cited by 4
- CategoryTheory.ComposableArrows.isComplex₂_iffstatement and proof · cited by 3
- CategoryTheory.ComposableArrows.scMapIsostatement and proof · cited by 3
- CategoryTheory.ComposableArrows.IsComplex.cokerToKerstatement and proof · cited by 3