Theorems · Definition · group theory

Rep.coindVEquiv

{k : Type u} →
  {G : Type v} →
    {H : Type w} →
      [inst : CommRing k] →
        [inst_1 : Monoid G] →
          [inst_2 : Monoid H] →
            (φ : G →* H) →
              (A : Rep.{max u w, u, v} k G) → ↥(Representation.coindV φ A.ρ) ≃ₗ[k] Rep.res φ (Rep.leftRegular k H) ⟶ A

If φ : G →* H and A : Rep k G then the k-submodule of functions f : H → A such that for all g : G, h : H, f (φ g * h) = A.ρ g (f h), is k-linearly equivalent to the G-representation morphisms k[H] ⟶ A.

Defined in

Mathlib.RepresentationTheory.Coinduced

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingMonoidMonoid