Theorems · Definition · group theory

AddMonoidHom.codRestrict

{M : Type u_1} →
  {N : Type u_2} →
    [inst : AddZeroClass M] →
      [inst_1 : AddZeroClass N] →
        {S : Type u_5} →
          [inst_2 : SetLike S N] →
            [inst_3 : AddSubmonoidClass S N] → (f : M →+ N) → (s : S) → (∀ (x : M), f x ∈ s) → M →+ ↥s

Restriction of an AddMonoidHom to an AddSubmonoid of the codomain.

Defined in

Mathlib.Algebra.Group.Submonoid.Operations

Cited by

5 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

AddZeroClassAddZeroClassSetLikeAddSubmonoidClass