Mathlib Map

Theorems · Definition · group theory

MulActionHom.inverse

{M : Type u_2} →
  {X : Type u_5} →
    [inst : SMul M X] →
      {Y₁ : Type u_8} →
        [inst_1 : SMul M Y₁] →
          (f : X →ₑ[id] Y₁) → (g : Y₁ → X) → Function.LeftInverse g ⇑f → Function.RightInverse g ⇑f → Y₁ →ₑ[id] X

The inverse of a bijective equivariant map is equivariant.

Defined in
Mathlib.GroupTheory.GroupAction.Hom
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
SMulSMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulSemiringActionHom.inverse · cited by 1MulSemiringActionHom.inve…DistribMulActionHom.inverse · cited by 0DistribMulActionHom.inver…MulActionHom.inverse_apply · cited by 0MulActionHom.inverse_applyMulActionHom.inverse_eq_inverse' · cited by 0MulActionHom.inverse_eq_i…MulDistribMulActionHom.inverse · cited by 0MulDistribMulActionHom.in…DFunLike.coe · cited by 62936DFunLike.coeMulActionHom · cited by 124MulActionHomMulActionHom.inverseCITED BYCITES

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Cited by5

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