Theorems · Theorem · category theory
HomologicalComplex.cyclesMap_comp
∀ {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 M : HomologicalComplex C c} (φ : K ⟶ L) (ψ : L ⟶ M) (i : ι)
[inst_2 : K.HasHomology i] [inst_3 : L.HasHomology i] [inst_4 : M.HasHomology i],
HomologicalComplex.cyclesMap (CategoryTheory.CategoryStruct.comp φ ψ) i =
CategoryTheory.CategoryStruct.comp (HomologicalComplex.cyclesMap φ i) (HomologicalComplex.cyclesMap ψ i)- Cited by
- 3 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.
Cites17
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.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- CategoryTheory.Functor.map_compproof · cited by 734
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- CategoryTheory.ShortComplex.cyclesproof · cited by 220
- HomologicalComplex.scproof · cited by 205
Cited by3
Results whose statement or proof uses this declaration.
- groupCohomology.cocyclesMap_id_compproof · cited by 1
- groupHomology.cyclesMap_id_compproof · cited by 0
- HomologicalComplex.cyclesMap_comp_assocproof · cited by 0