Theorems · Definition · category theory
HomologicalComplex.dTo
{ι : Type u_1} →
{V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
{c : ComplexShape ι} → (C : HomologicalComplex V c) → (j : ι) → C.xPrev j ⟶ C.X jThe differential mapping into C.X j, or zero if there isn't one.
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.Homstatement · cited by 32,603
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.dproof · cited by 598
- ComplexShape.prevproof · cited by 223
- HomologicalComplex.xPrevstatement · cited by 26
Cited by27
Results whose statement or proof uses this declaration.
- Homotopy.mkCoinductiveAux₂statement and proof · cited by 4
- Homotopy.mkInductiveAux₂statement and proof · cited by 4
- HomologicalComplex.Hom.sqTostatement · cited by 2
- HomologicalComplex.dTo_eqstatement and proof · cited by 2
- HomologicalComplex.Hom.comm_tostatement · cited by 2
- Homotopy.comp_nullHomotopicMapproof · cited by 1
- Homotopy.nullHomotopicMap_compproof · cited by 1
- HomologicalComplex.xPrevIsoSelf_comp_dTostatement · cited by 1
- HomologicalComplex.xPrevIso_comp_dTostatement · cited by 1
- HomologicalComplex.Hom.sqTo_leftstatement · cited by 0
- HomologicalComplex.Hom.sqTo_rightstatement · cited by 0
- HomologicalComplex.dTo_comp_dFromstatement · cited by 0