Theorems · Definition · group theory

AddMonoidHom.restrict

{M : Type u_1} →
  {N : Type u_2} →
    [inst : AddZeroClass M] →
      [inst_1 : AddZeroClass N] →
        {M' : AddSubmonoid M} → {N' : AddSubmonoid N} → {f : M →+ N} → Set.MapsTo ⇑f ↑M' ↑N' → ↥M' →+ ↥N'

Restrict the domain and codomain of an AddMonoidHom.

Defined in: Mathlib.Algebra.Group.Submonoid.Operations
Cited by: 1 results in Mathlib
Foundations: Depth 16 from the axioms · uses propext, Quot.sound
Assumes: AddZeroClass AddZeroClass

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Cites8

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

DFunLike.coestatement and proof · cited by 62,936
SetLike.coestatement and proof · cited by 8,199
AddMonoidHomstatement and proof · cited by 3,230
AddZeroClassstatement and proof · cited by 1,237
AddSubmonoidstatement and proof · cited by 1,178
Set.MapsTostatement and proof · cited by 732
AddMonoidHom.domRestrictproof · cited by 35
AddMonoidHom.codRestrictproof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

AddMonoidHom.restrict_injectivestatement and proof · cited by 0