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Theorems · Definition · group theory

Function.Injective.addLeftCancelSemigroup

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

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

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
AddAddLeftCancelSemigroup
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FunLike.addLeftCancelSemigroup · cited by 0FunLike.addLeftCancelSemi…Function.Injective.addCancelCommMonoid · cited by 0Injective.addCancelCommMo…Function.Injective.addLeftCancelMonoid · cited by 0Injective.addLeftCancelMo…AddSemigroup · cited by 136AddSemigroupIsLeftCancelAdd · cited by 72IsLeftCancelAddAddLeftCancelSemigroup · cited by 2AddLeftCancelSemigroupFunction.Injective.addSemigroup · cited by 0Injective.addSemigroupInjective.addLeftCancelSemigr…CITED BYCITES

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