Theorems · Definition · group theory
Rep.IsTrivial
{k : Type u} → {G : Type v} → [inst : Ring k] → [inst_1 : Monoid G] → Rep.{u_1, u, v} k G → PropA predicate for representations that fix every element.
- Defined in
- Mathlib.RepresentationTheory.Rep.Basic
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 34 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.
- Ringstatement and proof · cited by 7,463
- Monoidstatement and proof · cited by 3,887
- Repstatement and proof · cited by 843
- Rep.ρproof · cited by 356
- Representation.IsTrivialproof · cited by 14
Cited by45
Results whose statement or proof uses this declaration.
- groupCohomology.cocycles₁IsoOfIsTrivialstatement and proof · cited by 7
- groupHomology.cycles₁IsoOfIsTrivialstatement and proof · cited by 7
- groupCohomology.H0IsoOfIsTrivialstatement and proof · cited by 6
- groupCohomology.H1IsoOfIsTrivialstatement and proof · cited by 6
- groupHomology.H0IsoOfIsTrivialstatement and proof · cited by 5
- groupHomology.H1AddEquivOfIsTrivialstatement and proof · cited by 4
- groupHomology.H1ToTensorOfIsTrivialstatement and proof · cited by 3
- groupHomology.mkH1OfIsTrivialstatement and proof · cited by 3
- groupCohomology.π_comp_H0IsoOfIsTrivial_homstatement and proof · cited by 2
- groupHomology.π_comp_H0IsoOfIsTrivial_homstatement and proof · cited by 2
- groupCohomology.H1π_comp_H1IsoOfIsTrivial_homstatement and proof · cited by 2
- groupHomology.H1AddEquivOfIsTrivial_applystatement and proof · cited by 1