Theorems · Theorem · group theory

groupCohomology.H1IsoOfIsTrivial_inv_apply

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {A : Rep.{u, u, u} k G} [inst_2 : A.IsTrivial]
  (f : Additive G →+ ↑A),
  (CategoryTheory.ConcreteCategory.hom (groupCohomology.H1IsoOfIsTrivial A).inv) f =
    (CategoryTheory.ConcreteCategory.hom (groupCohomology.H1π A))
      ((CategoryTheory.ConcreteCategory.hom (groupCohomology.cocycles₁IsoOfIsTrivial A).inv) f)

Defined in: Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree
Cited by: 0 results in Mathlib
Foundations: Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group Rep.IsTrivial

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Submodulestatement · cited by 7,192
CategoryTheory.Iso.invstatement · cited by 6,514
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CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
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ModuleCat.carrierstatement · cited by 997
Repstatement and proof · cited by 843

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