Theorems · Theorem · group theory

groupHomology.coinvariantsMk_comp_H0Iso_inv_assoc

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G) {Z : ModuleCat k}
  (h : groupHomology.H0 A ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((Rep.coinvariantsMk k G).app A)
      (CategoryTheory.CategoryStruct.comp (groupHomology.H0Iso A).inv h) =
    CategoryTheory.CategoryStruct.comp (groupHomology.H0π A) h

Defined in: Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree
Cited by: 0 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing Group

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Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
RingHom.idstatement · cited by 18,349
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CommRingstatement and proof · cited by 17,173
LinearMapstatement · cited by 10,215
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
Groupstatement and proof · cited by 6,238
ModuleCatstatement and proof · cited by 1,429
ModuleCat.carrierstatement · cited by 997

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