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Theorems · Definition · group theory

Function.Injective.mulOneClass

{M₁ : Type u_1} →
  {M₂ : Type u_2} →
    [inst : Mul M₁] →
      [inst_1 : One M₁] →
        [inst_2 : MulOneClass M₂] →
          (f : M₁ → M₂) → Function.Injective f → f 1 = 1 → (∀ (x y : M₁), f (x * y) = f x * f y) → MulOneClass M₁

A type endowed with 1 and * is a MulOneClass, if it admits an injective map that preserves 1 and * to a MulOneClass. 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
MulOneMulOneClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.mulOneClass · cited by 6Finset.mulOneClassFunLike.mulOneClass · cited by 0FunLike.mulOneClassFunction.Injective.mulZeroOneClass · cited by 0Injective.mulZeroOneClassEquiv.mulOneClass · cited by 0Equiv.mulOneClassFunction.Injective.monoid · cited by 0Injective.monoidMulOneClass · cited by 1018MulOneClassInjective.mulOneClassCITED BYCITES

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