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Theorems · Definition · group theory

AddSubmonoidClass.subtype

{M : Type u_1} →
  {A : Type u_3} → [inst : AddZeroClass M] → [inst_1 : SetLike A M] → [hA : AddSubmonoidClass A M] → (S' : A) → ↥S' →+ M

The natural monoid hom from an AddSubmonoid of AddMonoid M to M.

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

Around this declaration

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

AddMonoidHom.domRestrict · cited by 35AddMonoidHom.domRestrictGradedRing.proj · cited by 23GradedRing.projAddSubmonoidClass.coe_finsetSum · cited by 15AddSubmonoidClass.coe_fin…DirectSum.coeAddMonoidHom · cited by 8DirectSum.coeAddMonoidHomSubsemiringClass.subtype · cited by 5SubsemiringClass.subtypeNonUnitalSubsemiringClass.subtype · cited by 5NonUnitalSubsemiringClass…DirectSum.coeAddMonoidHom_of · cited by 3DirectSum.coeAddMonoidHom…AddSubmonoidClass.coe_list_sum · cited by 2AddSubmonoidClass.coe_lis…AddSubmonoidClass.coe_multiset_sum · cited by 2AddSubmonoidClass.coe_mul…DirectSum.coeRingHom · cited by 1DirectSum.coeRingHomDirectSum.coeAddMonoidHom_eq_dfinsuppSum · cited by 1DirectSum.coeAddMonoidHom…DirectSum.coeRingHom_of · cited by 0DirectSum.coeRingHom_ofAddSubmonoidClass.coe_subtype · cited by 0AddSubmonoidClass.coe_sub…IsAddFreimanHom.subtypeVal · cited by 0IsAddFreimanHom.subtypeValAddSubmonoidClass.subtype_apply · cited by 0AddSubmonoidClass.subtype…AddMonoidHom · cited by 3230AddMonoidHomAddZeroClass · cited by 1237AddZeroClassSetLike · cited by 1084SetLikeAddSubmonoidClass · cited by 346AddSubmonoidClassAddSubmonoidClass.subtypeCITED BYCITES

Cites4

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

Cited by18

Results whose statement or proof uses this declaration.