Theorems · Theorem · group theory
Representation.IsTrivial.out
∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} {inst : Semiring k} {inst_1 : Monoid G} {inst_2 : AddCommMonoid V}
{inst_3 : Module k V} {ρ : Representation k G V} [self : ρ.IsTrivial] (g : G), ρ g = LinearMap.id- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
- Assumes
- Representation.IsTrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Monoidstatement and proof · cited by 3,887
- LinearMap.idstatement · cited by 625
- Representationstatement and proof · cited by 396
- Representation.IsTrivialstatement and proof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- Representation.isTrivial_defproof · cited by 4