Theorems · Definition · number theory
MulChar.equivToUnitHom
{R : Type u_1} → [inst : CommMonoid R] → {R' : Type u_2} → [inst_1 : CommMonoidWithZero R'] → MulChar R R' ≃ (Rˣ →* R'ˣ)The equivalence between multiplicative characters and homomorphisms of unit groups.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- CommMonoidWithZerostatement and proof · cited by 913
- MulCharstatement · cited by 186
- MulChar.toUnitHomproof · cited by 14
- MulChar.ofUnitHomproof · cited by 10
Cited by21
Results whose statement or proof uses this declaration.
- MulChar.coe_equivToUnitHomstatement · cited by 12
- MulChar.mulEquivToUnitHomproof · cited by 7
- MulChar.equivToUnitHom_symm_coestatement · cited by 6
- DirichletCharacter.changeLevel_transproof · cited by 6
- DirichletCharacter.changeLevel_injectiveproof · cited by 5
- DirichletCharacter.factorsThrough_iff_ker_unitsMapproof · cited by 4
- MulChar.domRestrict_applyproof · cited by 3
- DirichletCharacter.changeLevel_eq_cast_of_dvdproof · cited by 3
- MulChar.mulEquivToUnitHom_applystatement · cited by 3
- MulChar.domRestrict_ofUnitHomproof · cited by 2
- DirichletCharacter.changeLevel_selfproof · cited by 2
- MulChar.domRestrictHom_surjectiveproof · cited by 1