Theorems · Definition · group theory

Representation.finsuppToCoinvariants

{k : Type u_6} →
  {G : Type u_7} →
    {V : Type u_8} →
      [inst : CommRing k] →
        [inst_1 : Group G] →
          [inst_2 : AddCommGroup V] →
            [inst_3 : Module k V] →
              (ρ : Representation k G V) → (α : Type u_9) → (α →₀ ρ.Coinvariants) →ₗ[k] (ρ.finsupp α).Coinvariants

Given a G-representation (V, ρ) and a type α, this is the map (α →₀ V_G) →ₗ (α →₀ V)_G sending single a ⟦v⟧ ↦ ⟦single a v⟧.

Defined in

Mathlib.RepresentationTheory.Coinvariants

Cited by

2 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupAddCommGroupModule