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Theorems · Definition · group theory

Function.Injective.leftCancelSemigroup

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

A type endowed with * is a left cancel semigroup, if it admits an injective map that preserves * to a left cancel 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
MulLeftCancelSemigroup
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FunLike.leftCancelSemigroup · cited by 0FunLike.leftCancelSemigro…Function.Injective.cancelCommMonoid · cited by 0Injective.cancelCommMonoidFunction.Injective.leftCancelMonoid · cited by 0Injective.leftCancelMonoidSemigroup · cited by 202SemigroupIsLeftCancelMul · cited by 51IsLeftCancelMulLeftCancelSemigroup · cited by 3LeftCancelSemigroupFunction.Injective.semigroup · cited by 0Injective.semigroupInjective.leftCancelSemigroupCITED BYCITES

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