Theorems · Inductive type · group theory
Representation.IsTrivial
{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 V → PropA predicate for representations that fix every element.
- Defined in
- Mathlib.RepresentationTheory.Basic
- Cited by
- 14 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 · cited by 20,661
- Semiringstatement · cited by 13,802
- AddCommMonoidstatement · cited by 12,281
- Monoidstatement · cited by 3,887
- Representationstatement · cited by 396
Cited by22
Results whose statement or proof uses this declaration.
- Rep.IsTrivialproof · cited by 37
- groupHomology.H1CoresCoinfOfTrivialstatement and proof · cited by 7
- Representation.isTrivial_applystatement and proof · cited by 4
- Representation.isTrivial_defstatement and proof · cited by 4
- Rep.ofQuotientstatement and proof · cited by 4
- Representation.ofQuotientstatement and proof · cited by 3
- Rep.descstatement and proof · cited by 3
- Rep.resOfQuotientIsostatement and proof · cited by 2
- Representation.IsTrivial.outstatement and proof · cited by 1
- groupHomology.H1CoresCoinfOfTrivial_exactstatement and proof · cited by 1
- Representation.ofQuotient.congr_simpstatement and proof · cited by 0
- Representation.ofQuotient_coe_applystatement and proof · cited by 0