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Theorems · Definition · group theory

Function.Injective.addSemigroup

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

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

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
AddAddSemigroup
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Around this declaration

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Finset.addSemigroup · cited by 0Finset.addSemigroupFunction.Injective.addCommSemigroup · cited by 0Injective.addCommSemigroupEquiv.addSemigroup · cited by 0Equiv.addSemigroupFunLike.addSemigroup · cited by 0FunLike.addSemigroupFunction.Injective.addLeftCancelSemigroup · cited by 0Injective.addLeftCancelSe…Function.Injective.addMonoid · cited by 0Injective.addMonoidFunction.Injective.addRightCancelSemigroup · cited by 0Injective.addRightCancelS…AddSemigroup · cited by 136AddSemigroupInjective.addSemigroupCITED BYCITES

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