Theorems · Theorem · category theory
HomologicalComplex.p_opcyclesMap
∀ {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} {K L : HomologicalComplex C c} (φ : K ⟶ L) (i : ι) [inst_2 : K.HasHomology i]
[inst_3 : L.HasHomology i],
CategoryTheory.CategoryStruct.comp (K.pOpcycles i) (HomologicalComplex.opcyclesMap φ i) =
CategoryTheory.CategoryStruct.comp (φ.f i) (L.pOpcycles i)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- 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.Hom.fstatement · cited by 845
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- HomologicalComplex.opcyclesstatement · cited by 153
- HomologicalComplex.shortComplexFunctorproof · cited by 72
Cited by7
Results whose statement or proof uses this declaration.
- HomologicalComplex.p_opcyclesMap_assocproof · cited by 7
- CategoryTheory.ShortComplex.ShortExact.δ_applyproof · cited by 2
- HomologicalComplex.singleObjOpcyclesSelfIso_hom_naturalityproof · cited by 2
- CategoryTheory.ShortComplex.ShortExact.δ_eqproof · cited by 1
- CochainComplex.isSplitMono_from_singleFunctor_obj_of_injectiveproof · cited by 1
- CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succproof · cited by 0
- CochainComplex.ConnectData.homologyMap_map_of_eq_succproof · cited by 0