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Theorems · Definition · group theory

Function.Surjective.commMagma

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

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

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
MulCommMagma
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Function.Surjective.nonUnitalNonAssocCommSemiring · cited by 0Surjective.nonUnitalNonAs…Function.Surjective.nonAssocCommSemiring · cited by 0Surjective.nonAssocCommSe…Function.Surjective.commSemigroup · cited by 0Surjective.commSemigroupCommMagma · cited by 57CommMagmaSurjective.commMagmaCITED BYCITES

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