Theorems · Definition · group theory
CoxeterSystem.mulEquiv
{B : Type u_1} → {M : CoxeterMatrix B} → {W : Type u_2} → [inst : Group W] → CoxeterSystem M W → W ≃* M.GroupThe isomorphism between W and the Coxeter group associated to M.
- Defined in
- Mathlib.GroupTheory.Coxeter.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- MulEquivstatement · cited by 1,142
- CoxeterMatrixstatement and proof · cited by 140
- CoxeterSystemstatement and proof · cited by 126
- CoxeterMatrix.Groupstatement · cited by 11
Cited by11
Results whose statement or proof uses this declaration.
- CoxeterSystem.simpleproof · cited by 73
- CoxeterSystem.simple_mul_simple_selfproof · cited by 9
- CoxeterSystem.extstatement and proof · cited by 2
- CoxeterSystem.mapproof · cited by 2
- CoxeterSystem.reindexproof · cited by 2
- CoxeterSystem.simple_mul_simple_powproof · cited by 1
- CoxeterSystem.subgroup_closure_range_simpleproof · cited by 1
- CoxeterSystem.simple_determines_coxeterSystemproof · cited by 0
- CoxeterSystem.ext_iffstatement and proof · cited by 0
- CoxeterSystem.map_mulEquivstatement and proof · cited by 0
- CoxeterSystem.reindex_mulEquivstatement and proof · cited by 0