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Theorems · Definition · group theory

Function.Injective.involutiveInv

{M₂ : Type u_2} →
  {M₁ : Type u_3} →
    [inst : Inv M₁] →
      [inst_1 : InvolutiveInv M₂] →
        (f : M₁ → M₂) → Function.Injective f → (∀ (x : M₁), f x⁻¹ = (f x)⁻¹) → InvolutiveInv M₁

A type has an involutive inversion if it admits a surjective map that preserves ⁻¹ to a type which has an involutive inversion. See note [reducible non-instances]

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
InvInvolutiveInv
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Around this declaration

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

FunLike.involutiveInv · cited by 0FunLike.involutiveInvFunction.Injective.divisionMonoid · cited by 0Injective.divisionMonoidSubmonoid.involutiveInv · cited by 0Submonoid.involutiveInvInvolutiveInv · cited by 102InvolutiveInvInjective.involutiveInvCITED BYCITES

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