Theorems · Definition · group theory

Function.Injective.addCommSemigroup

{M₁ : Type u_1} →
  {M₂ : Type u_2} →
    [inst : Add M₁] →
      [inst_1 : AddCommSemigroup M₂] →
        (f : M₁ → M₂) → Function.Injective f → (∀ (x y : M₁), f (x + y) = f x + f y) → AddCommSemigroup M₁

A type endowed with + is an additive commutative semigroup,if it admits an injective map that preserves + to an additive commutative semigroup.

Defined in

Mathlib.Algebra.Group.InjSurj

Cited by

0 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

AddAddCommSemigroup