Mathlib Map

Theorems · Definition · group theory

MonoidHom.submonoidMap

{M : Type u_1} →
  {N : Type u_2} →
    [inst : MulOneClass M] → [inst_1 : MulOneClass N] → (f : M →* N) → (M' : Submonoid M) → ↥M' →* ↥(Submonoid.map f M')

The MonoidHom from a Submonoid to its image. See MulEquiv.SubmonoidMap for a variant for MulEquivs.

Defined in
Mathlib.Algebra.Group.Submonoid.Operations
Cited by
4 results in Mathlib
Foundations
Depth 16 from the axioms · uses no axioms
Assumes
MulOneClassMulOneClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsLocalization.toInvSubmonoid · cited by 11IsLocalization.toInvSubmo…MonoidHom.subgroupMap · cited by 8MonoidHom.subgroupMapMonoidHom.submonoidMap_surjective · cited by 2MonoidHom.submonoidMap_su…IsLocalization.toInvSubmonoid_mul · cited by 1IsLocalization.toInvSubmo…MonoidHom.submonoidMap_apply_coe · cited by 0MonoidHom.submonoidMap_ap…MonoidHom.submonoidMap_injective · cited by 0MonoidHom.submonoidMap_in…DFunLike.coe · cited by 62936DFunLike.coeMonoidHom · cited by 3629MonoidHomSubmonoid · cited by 3086SubmonoidMulOneClass · cited by 1018MulOneClassSubmonoid.map · cited by 190Submonoid.mapMonoidHom.submonoidMapCITED BYCITES

Cites5

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

Cited by6

Results whose statement or proof uses this declaration.