Theorems · Definition · number theory
MulChar.mulCharEquiv
(M : Type u_1) →
(R : Type u_2) →
[inst : CommMonoid M] →
[inst_1 : CommRing R] →
[Finite M] → [HasEnoughRootsOfUnity R (Monoid.exponent Mˣ)] → MulChar (MulChar M R) R ≃* MˣThe MulEquiv between the double dual MulChar (MulChar M R) R of M and Mˣ.
The image m of η : MulChar (MulChar M R) R is such that, for all R-valued multiplicative
character χ of M, we have χ m = η χ, see MulChar.apply_mulCharEquiv.
- Defined in
- Mathlib.NumberTheory.MulChar.Duality
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finitestatement and proof · cited by 3,029
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- MulEquivstatement · cited by 1,142
- MulEquiv.symmproof · cited by 482
- MulCharstatement · cited by 186
- Monoid.exponentstatement and proof · cited by 128
- HasEnoughRootsOfUnitystatement and proof · cited by 56
- MulEquiv.transproof · cited by 53
- toUnitsproof · cited by 8
- MulChar.mulEquivToUnitHomproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- MulChar.mulCharEquiv_symm_apply_applystatement and proof · cited by 1
- MulChar.apply_mulCharEquivstatement and proof · cited by 0