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Theorems · Definition · group theory

Function.Injective.involutiveNeg

{M₂ : Type u_2} →
  {M₁ : Type u_3} →
    [inst : Neg M₁] →
      [inst_1 : InvolutiveNeg M₂] →
        (f : M₁ → M₂) → Function.Injective f → (∀ (x : M₁), f (-x) = -f x) → InvolutiveNeg M₁

A type has an involutive negation if it admits a surjective map that preserves - to a type which has an involutive negation.

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
0 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
NegInvolutiveNeg
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FunLike.involutiveNeg · cited by 0FunLike.involutiveNegFunction.Injective.hasDistribNeg · cited by 0Injective.hasDistribNegFunction.Injective.subtractionMonoid · cited by 0Injective.subtractionMono…AddSubmonoid.involutiveNeg · cited by 0AddSubmonoid.involutiveNegInvolutiveNeg · cited by 151InvolutiveNegInjective.involutiveNegCITED BYCITES

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