Theorems · Theorem · group theory
Rep.coindToInd_apply
∀ {k : Type u} {G : Type v} [inst : CommRing k] [inst_1 : Group G] {S : Subgroup G} (A : Rep.{w, u, v} k ↥S)
[inst_2 : S.FiniteIndex] (f : ↑(Rep.coind.{u, v, v, w} S.subtype A)),
A.coindToInd f = ∑ g, g.liftOn (fun g => (Representation.IndV.mk S.subtype A.ρ g) (↑f g)) ⋯- Defined in
- Mathlib.RepresentationTheory.FiniteIndex
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- Groupstatement and proof · cited by 6,238
- Finset.sumstatement · cited by 5,195
- Subgroupstatement and proof · cited by 3,593
- Finset.univstatement · cited by 3,473
- TensorProductstatement · cited by 2,545
- Repstatement and proof · cited by 843
- Rep.Vstatement and proof · cited by 695
Cited by2
Results whose statement or proof uses this declaration.
- Rep.coindToInd_indToCoindproof · cited by 1
- Rep.coindToInd_of_support_subset_orbitproof · cited by 1