Theorems · Theorem · group theory
ContinuousCohomology.cochainsMap_comp
∀ {k : Type u} {G H K : Type v} [inst : Ring k] [inst_1 : TopologicalSpace k] [inst_2 : Group G]
[inst_3 : TopologicalSpace G] [inst_4 : IsTopologicalGroup G] [inst_5 : Group H] [inst_6 : TopologicalSpace H]
[inst_7 : IsTopologicalGroup H] [inst_8 : Group K] [inst_9 : TopologicalSpace K] [inst_10 : IsTopologicalGroup K]
{X : TopRep k G} {Y : TopRep k H} {Z : TopRep k K} (φ : H →ₜ* G) (ψ : K →ₜ* H) (f : TopRep.res (↑φ) X ⟶ Y)
(g : TopRep.res (↑ψ) Y ⟶ Z),
ContinuousCohomology.cochainsMap (φ.comp ψ) (CategoryTheory.CategoryStruct.comp ((TopRep.resFunctor ↑ψ).map f) g) =
CategoryTheory.CategoryStruct.comp (ContinuousCohomology.cochainsMap φ f) (ContinuousCohomology.cochainsMap ψ g)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- TopologicalSpacestatement and proof · cited by 24,529
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Ringstatement and proof · cited by 7,463
- Groupstatement and proof · cited by 6,238
- HomologicalComplex.Xproof · cited by 1,839
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement · cited by 1,016
- ModuleCat.carrierproof · cited by 997
- IsTopologicalGroupstatement and proof · cited by 469
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousCohomology.cochainsMap_comp_assocproof · cited by 0