Theorems · Theorem · group theory
Representation.isTrivial_apply
∀ {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) [ρ.IsTrivial] (g : G) (x : V), (ρ g) x = x- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Quot.sound
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 and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Monoidstatement and proof · cited by 3,887
- Representationstatement and proof · cited by 396
- Representation.IsTrivialstatement and proof · cited by 14
- Representation.isTrivial_defproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- groupCohomology.d₀₁_eq_zeroproof · cited by 1
- groupCohomology.cocycles₁_map_mul_of_isTrivialproof · cited by 0
- groupCohomology.mem_cocycles₁_of_addMonoidHomproof · cited by 0
- Representation.invariants_eq_topproof · cited by 0