Theorems · Theorem · category theory
CategoryTheory.ComposableArrows.isComplex_of_iso
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{n : ℕ} {S₁ S₂ : CategoryTheory.ComposableArrows C n} (e : S₁ ≅ S₂), S₁.IsComplex → S₂.IsComplex- Defined in
- Mathlib.Algebra.Homology.ExactSequence
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ComposableArrowsstatement and proof · cited by 627
- CategoryTheory.homOfLEproof · cited by 554
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ComposableArrows.exact_of_isoproof · cited by 2
- CategoryTheory.ComposableArrows.isComplex_iff_of_isoproof · cited by 0