Theorems · Definition · group theory
Rep.trivial
(k : Type u) →
(G : Type v) →
[inst : Semiring k] →
[inst_1 : Monoid G] → (V : Type w) → [inst_2 : AddCommGroup V] → [Module k V] → Rep.{w, u, v} k GThe trivial k-linear G-representation on a k-module V.
- Defined in
- Mathlib.RepresentationTheory.Rep.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommGroupstatement and proof · cited by 12,871
- Monoidstatement and proof · cited by 3,887
- Repstatement · cited by 843
- Rep.ofproof · cited by 57
- Representation.trivialproof · cited by 34
Cited by42
Results whose statement or proof uses this declaration.
- Rep.trivialFunctorproof · cited by 10
- Rep.FiniteCyclicGroup.resolutionstatement · cited by 6
- Rep.standardComplex.forget₂ToModuleCatHomotopyEquivstatement · cited by 4
- Rep.FiniteCyclicGroup.resolution.πstatement and proof · cited by 3
- Rep.standardComplex.forget₂ToModuleCatHomotopyEquiv_f_0_eqstatement · cited by 2
- Rep.standardComplex.εstatement · cited by 2
- Rep.standardComplex.εToSingle₀statement and proof · cited by 2
- Rep.FiniteCyclicGroup.coinvariantsTensorResolutionIsostatement · cited by 2
- Rep.FiniteCyclicGroup.homResolutionIsostatement · cited by 2
- Rep.barResolutionstatement · cited by 1
- Rep.leftRegularTensorTrivialIsoFreestatement · cited by 1
- Rep.linearizationTrivialIsostatement · cited by 1