Theorems · Definition · category theory
HomologicalComplex.shortComplexFunctor
(C : Type u_1) →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
{ι : Type u_2} →
(c : ComplexShape ι) → ι → CategoryTheory.Functor (HomologicalComplex C c) (CategoryTheory.ShortComplex C)The functor HomologicalComplex C c ⥤ ShortComplex C which sends a homological
complex K to the short complex K.X (c.prev i) ⟶ K.X i ⟶ K.X (c.next i).
- Cited by
- 72 results in Mathlib
- Foundations
- Depth 21 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
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.ShortComplexstatement · cited by 1,850
- HomologicalComplexstatement · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- ComplexShape.nextproof · cited by 297
- ComplexShape.prevproof · cited by 223
- HomologicalComplex.shortComplexFunctor'proof · cited by 42
Cited by84
Results whose statement or proof uses this declaration.
- HomologicalComplex.scproof · cited by 205
- HomologicalComplex.homologyMapproof · cited by 102
- HomologicalComplex.cyclesMapproof · cited by 59
- HomologicalComplex.opcyclesMapproof · cited by 47
- HomologicalComplex.natIsoSc'statement and proof · cited by 31
- CochainComplex.shiftShortComplexFunctorIsostatement · cited by 12
- HomologicalComplex.homologyπ_naturalityproof · cited by 11
- HomologicalComplex.cyclesMap_iproof · cited by 9
- HomologicalComplex.homologyMap_compproof · cited by 7
- HomologicalComplex.homologyι_naturalityproof · cited by 7
- HomologicalComplex.p_opcyclesMapproof · cited by 7
- quasiIsoAt_iff_isIso_homologyMapproof · cited by 6