Theorems · Theorem · category theory
HomologicalComplex.cyclesMap_i_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.X i ⟶ Z),
CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap φ i)
(CategoryTheory.CategoryStruct.comp (L.iCycles i) h) =
CategoryTheory.CategoryStruct.comp (K.iCycles i) (CategoryTheory.CategoryStruct.comp (φ.f i) h)- Cited by
- 8 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.
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 and proof · 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.cyclesstatement · cited by 164
- HomologicalComplex.iCyclesstatement and proof · cited by 80
Cited by8
Results whose statement or proof uses this declaration.
- groupCohomology.map_H0Iso_hom_fproof · cited by 3
- groupHomology.cyclesMap_comp_cyclesIso₀_homproof · cited by 3
- groupCohomology.cocyclesMap_cocyclesIso₀_hom_fproof · cited by 2
- groupCohomology.cocyclesMap_comp_isoCocycles₁_homproof · cited by 2
- groupCohomology.cocyclesMap_comp_isoCocycles₂_homproof · cited by 2
- groupHomology.cyclesMap_comp_isoCycles₁_homproof · cited by 2
- groupHomology.cyclesMap_comp_isoCycles₂_homproof · cited by 2
- HomologicalComplex.extendCyclesIso_hom_naturalityproof · cited by 1