Theorems · Definition · group theory

Representation.Coinvariants.lift

{k : Type u_1} →
  {G : Type u_2} →
    {V : Type u_3} →
      {W : Type u_4} →
        [inst : CommRing k] →
          [inst_1 : Monoid G] →
            [inst_2 : AddCommGroup V] →
              [inst_3 : Module k V] →
                [inst_4 : AddCommGroup W] →
                  [inst_5 : Module k W] →
                    (ρ : Representation k G V) → (f : V →ₗ[k] W) → (∀ (x : G), f ∘ₗ ρ x = f) → ρ.Coinvariants →ₗ[k] W

A G-invariant linear map induces a linear map out of the coinvariants of a G-representation.

Defined in

Mathlib.RepresentationTheory.Coinvariants

Cited by

9 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingMonoidAddCommGroupModuleAddCommGroupModule