Theorems · Definition · group theory
Submonoid.unitsEquivUnitsType
{M : Type u_1} → [inst : Monoid M] → (S : Submonoid M) → ↥S.units ≃* (↥S)ˣThe equivalence between the subgroup of units of S and the type of units of S.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement · cited by 3,593
- Submonoidstatement and proof · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- MulEquivstatement · cited by 1,142
- Units.coeHomproof · cited by 44
- Submonoid.unitsstatement and proof · cited by 40
- Submonoid.coe_val_mul_coe_inv_valproof · cited by 0
- Submonoid.mk_inv_mul_mk_eq_oneproof · cited by 0
- Submonoid.mk_mul_mk_inv_eq_oneproof · cited by 0
Cited by10
Results whose statement or proof uses this declaration.
- MulChar.domRestrict_ofUnitHomstatement and proof · cited by 2
- Submonoid.val_unitsEquivUnitsType_symm_apply_coestatement and proof · cited by 1
- DirichletCharacter.mem_annihilator_iff_mem_closureproof · cited by 1
- MulChar.domRestrictHom_surjectiveproof · cited by 1
- Submonoid.unitsEquivIsUnitSubmonoidproof · cited by 1
- Submonoid.val_unitsEquivUnitsType_apply_coestatement and proof · cited by 0
- MulChar.restrict_ofUnitHomstatement · cited by 0
- Subgroup.unitsEquivSelfproof · cited by 0
- Submonoid.val_inv_unitsEquivUnitsType_apply_coestatement and proof · cited by 0
- Submonoid.val_inv_unitsEquivUnitsType_symm_apply_coestatement and proof · cited by 0