Theorems · Theorem · category theory
HomologicalComplex.p_opcyclesMap_assoc
∀ {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] {Z : C} (h : L.opcycles i ⟶ Z),
CategoryTheory.CategoryStruct.comp (K.pOpcycles i)
(CategoryTheory.CategoryStruct.comp (HomologicalComplex.opcyclesMap φ i) h) =
CategoryTheory.CategoryStruct.comp (φ.f i) (CategoryTheory.CategoryStruct.comp (L.pOpcycles i) h)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Category.assocproof · cited by 6,433
- 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 and proof · cited by 845
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- HomologicalComplex.opcyclesstatement and proof · cited by 153
- HomologicalComplex.pOpcyclesstatement and proof · cited by 71
Cited by7
Results whose statement or proof uses this declaration.
- HomologicalComplex.restrictionToTruncGE'_naturalityproof · cited by 3
- HomologicalComplex.opcyclesMap_comp_descOpcyclesproof · cited by 2
- CategoryTheory.ProjectiveResolution.fromLeftDerivedZero'_naturalityproof · cited by 2
- HomologicalComplex.opcyclesToCycles_naturalityproof · cited by 1
- HomologicalComplex.opcycles_right_exactproof · cited by 1
- CochainComplex.ConnectData.homologyMap_map_of_eq_neg_succproof · cited by 0
- CochainComplex.ConnectData.homologyMap_map_of_eq_succproof · cited by 0