Theorems · Definition · group theory

Function.Injective.commSemigroup

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

A type endowed with * is a commutative semigroup, if it admits an injective map that preserves * to a commutative semigroup. See note [reducible non-instances].

Defined in

Mathlib.Algebra.Group.InjSurj

Cited by

0 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

MulCommSemigroup