Theorems · Definition · group theory
ofUnits_units_gci
{M : Type u_1} → [inst : Monoid M] → GaloisCoinsertion Subgroup.ofUnits Submonoid.unitsA Galois coinsertion exists between the coercion from a subgroup of units to a submonoid and the reduction from a submonoid to its unit group.
- Defined in
- Mathlib.Algebra.Group.Submonoid.Units
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Subgroupstatement · cited by 3,593
- Submonoidstatement · cited by 3,086
- Unitsstatement · cited by 2,804
- Submonoid.unitsstatement · cited by 40
- GaloisCoinsertionstatement · cited by 35
- Subgroup.ofUnitsstatement · cited by 31
- Submonoid.units_monoproof · cited by 0
- Subgroup.ofUnits_monoproof · cited by 0
- Submonoid.ofUnits_units_leproof · cited by 0
- GaloisCoinsertion.monotoneIntroproof · cited by 0
- Subgroup.units_ofUnits_eqproof · cited by 0
Cited by10
Results whose statement or proof uses this declaration.
- ofUnits_units_gcproof · cited by 11
- Submonoid.units_botproof · cited by 0
- Submonoid.units_left_inverseproof · cited by 0
- Subgroup.ofUnits_inf_unitsproof · cited by 0
- Subgroup.ofUnits_injectiveproof · cited by 0
- Subgroup.ofUnits_le_ofUnits_iffproof · cited by 0
- Submonoid.units_surjectiveproof · cited by 0
- Subgroup.ofUnits_right_inverseproof · cited by 0
- Subgroup.ofUnits_strictMonoproof · cited by 0
- Subgroup.ofUnits_sup_unitsproof · cited by 0