Theorems · Definition · group theory
Representation.trivial
(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] → Representation k G VThe trivial representation of G on a k-module V.
- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Monoidstatement and proof · cited by 3,887
- Representationstatement · cited by 396
Cited by42
Results whose statement or proof uses this declaration.
- Rep.trivialproof · cited by 20
- Representation.LinearizeMonoidal.εstatement · cited by 8
- Representation.LinearizeMonoidal.ηstatement · cited by 8
- Representation.TensorProduct.lidstatement · cited by 7
- Representation.TensorProduct.ridstatement · cited by 7
- Representation.LinearizeMonoidal.ε_toLinearMapstatement · cited by 5
- Representation.LinearizeMonoidal.η_toLinearMapstatement · cited by 5
- Representation.ofMulActionSubsingletonEquivTrivialstatement · cited by 2
- Representation.leftRegularTensorTrivialIsoFreestatement · cited by 2
- Representation.linearizeTrivialIsostatement · cited by 2
- Representation.leftRegularTensorTrivialIsoFree_symm_apply_single_singlestatement · cited by 1
- Representation.ofMulActionSubsingletonEquivTrivial_applystatement · cited by 0