Theorems · Theorem · group theory

groupHomology.isoShortComplexH2_inv

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G),
  (groupHomology.isoShortComplexH2 A).inv =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.ShortComplex.homMk (groupHomology.chainsIso₃ A).inv (groupHomology.chainsIso₂ A).inv
        (groupHomology.chainsIso₁ A).inv ⋯ ⋯)
      ((HomologicalComplex.natIsoSc' (ModuleCat k) (ComplexShape.down ℕ) 3 2 1 groupHomology.isoShortComplexH2._proof_1
              groupHomology.isoShortComplexH2._proof_2).inv.app
        (groupHomology.inhomogeneousChains A))

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree

Cited by

0 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroup