Theorems · Definition · number theory
MulChar.mulEquivToUnitHom
{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 as a multiplicative equivalence.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 31 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.
- Equivproof · cited by 8,337
- MonoidHomstatement and proof · cited by 3,629
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- CommMonoidWithZerostatement and proof · cited by 913
- MulCharstatement and proof · cited by 186
- MulChar.equivToUnitHomproof · cited by 20
Cited by9
Results whose statement or proof uses this declaration.
- MulChar.subgroupOrderIsoSubgroupMulCharproof · cited by 6
- MulChar.mulEquivToUnitHom_applystatement and proof · cited by 3
- MulChar.mulCharEquivproof · cited by 2
- MulChar.mulEquiv_unitsproof · cited by 2
- MulChar.mulCharEquiv_symm_apply_applyproof · cited by 1
- MulChar.card_subgroupOrderIsoSubgroupMulCharproof · cited by 1
- MulChar.mem_subgroupOrderIsoSubgroupMulChar_iffproof · cited by 0
- MulChar.mem_subgroupOrderIsoSubgroupMulChar_symm_iffproof · cited by 0
- MulChar.mulEquivToUnitHom_symm_applystatement and proof · cited by 0