Theorems · Definition · group theory

Rep.resCoindAdjunction

(k : Type u) →
  {G : Type v} →
    {H : Type w} →
      [inst : CommRing k] →
        [inst_1 : Monoid G] → [inst_2 : Monoid H] → (φ : G →* H) → Rep.resFunctor φ ⊣ Rep.coindFunctor k φ

Given a monoid homomorphism φ : G →* H, the coinduction functor Rep k G ⥤ Rep k H is right adjoint to the restriction functor along φ.

Defined in

Mathlib.RepresentationTheory.Coinduced

Cited by

3 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingMonoidMonoid