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Theorems · Definition · group theory

AddChar.toAddMonoidHom

{A : Type u_1} → {M : Type u_3} → [inst : AddMonoid A] → [inst_1 : Monoid M] → AddChar A M → A →+ Additive M

Interpret an additive character as a monoid homomorphism.

Defined in
Mathlib.Algebra.Group.AddChar
Cited by
5 results in Mathlib
Foundations
Depth 16 from the axioms · uses Quot.sound
Assumes
AddMonoidMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup.strictPeriods · cited by 63Subgroup.strictPeriodsAddChar.toAddMonoidHomEquiv · cited by 8AddChar.toAddMonoidHomEqu…Subgroup.strictWidthInfty_pos_iff · cited by 5Subgroup.strictWidthInfty…AddChar.compAddMonoidHom · cited by 5AddChar.compAddMonoidHomSubgroup.strictPeriods_le_periods · cited by 3Subgroup.strictPeriods_le…AddChar.zmodAddEquiv · cited by 1AddChar.zmodAddEquivAddChar.toAddMonoidHom_apply · cited by 0AddChar.toAddMonoidHom_ap…Matrix.GeneralLinearGroup.injective_upperRightHom · cited by 0GeneralLinearGroup.inject…AddChar.coe_toAddMonoidHom · cited by 0AddChar.coe_toAddMonoidHomMonoid · cited by 3887MonoidAddMonoidHom · cited by 3230AddMonoidHomAddMonoid · cited by 2864AddMonoidAdditive · cited by 356AdditiveAddChar · cited by 286AddCharAddChar.toFun · cited by 2AddChar.toFunAddChar.map_add_eq_mul' · cited by 1AddChar.map_add_eq_mul'AddChar.map_zero_eq_one' · cited by 1AddChar.map_zero_eq_one'AddChar.toAddMonoidHomCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by9

Results whose statement or proof uses this declaration.