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Theorems · Definition · group theory

Function.Surjective.addCommMagma

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

A type endowed with + is an additive commutative semigroup, if it admits a surjective map that preserves + from an additive commutative semigroup.

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
AddAddCommMagma
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Function.Surjective.addCommSemigroup · cited by 0Surjective.addCommSemigro…AddCommMagma · cited by 32AddCommMagmaSurjective.addCommMagmaCITED BYCITES

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