Theorems · Definition · group theory
Rep.toCoinvariants
{k : Type u} →
{G : Type v} →
[inst : CommRing k] → [inst_1 : Group G] → Rep.{w, u, v} k G → (S : Subgroup G) → [S.Normal] → Rep.{w, u, v} k GGiven a normal subgroup S ≤ G, a G-representation A induces a G-representation on
the S-coinvariants A_S.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingGroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Repstatement and proof · cited by 843
- Rep.ρproof · cited by 356
- Subgroup.Normalstatement and proof · cited by 334
- Rep.ofproof · cited by 57
- Representation.toCoinvariantsproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Rep.toCoinvariantsMkQstatement · cited by 4
- Rep.quotientToCoinvariantsproof · cited by 3
- Rep.coinvariantsShortComplex_gstatement · cited by 0
- Rep.quotientToCoinvariantsFunctor_map_hom_toLinearMapstatement · cited by 0
- groupHomology.H1CoresCoinf_exactproof · cited by 0
- Rep.toCoinvariants.congr_simpstatement and proof · cited by 0
- Rep.coinvariantsShortComplex_X₃statement · cited by 0