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Theorems · Definition · group theory

SubmonoidClass.subtype

{M : Type u_1} →
  {A : Type u_3} → [inst : MulOneClass M] → [inst_1 : SetLike A M] → [hA : SubmonoidClass A M] → (S' : A) → ↥S' →* M

The natural monoid hom from a submonoid of monoid M to M.

Defined in
Mathlib.Algebra.Group.Submonoid.Defs
Cited by
11 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
Assumes
MulOneClassSetLikeSubmonoidClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MonoidHom.domRestrict · cited by 59MonoidHom.domRestrictMulChar.domRestrict · cited by 8MulChar.domRestrictSubsemiringClass.subtype · cited by 5SubsemiringClass.subtypeSubmonoidClass.coe_finsetProd · cited by 4SubmonoidClass.coe_finset…MulChar.domRestrict_apply · cited by 3MulChar.domRestrict_applySubringClass.subtype · cited by 3SubringClass.subtypeSubmonoidClass.coe_list_prod · cited by 2SubmonoidClass.coe_list_p…SubmonoidClass.coe_multiset_prod · cited by 2SubmonoidClass.coe_multis…MonoidHom.isUnit_eqLocusM_mk_iff · cited by 2MonoidHom.isUnit_eqLocusM…IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq · cited by 1HeightOneSpectrum.valuati…SubmonoidClass.coe_subtype · cited by 0SubmonoidClass.coe_subtypeIsUnit.coe · cited by 0IsUnit.coeIsMulFreimanHom.subtypeVal · cited by 0IsMulFreimanHom.subtypeValSubmonoidClass.subtype_apply · cited by 0SubmonoidClass.subtype_ap…SubmonoidClass.subtype_injective · cited by 0SubmonoidClass.subtype_in…MonoidHom · cited by 3629MonoidHomSetLike · cited by 1084SetLikeMulOneClass · cited by 1018MulOneClassSubmonoidClass · cited by 60SubmonoidClassSubmonoidClass.subtypeCITED BYCITES

Cites4

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

Cited by15

Results whose statement or proof uses this declaration.