Mathlib Map

Theorems · Definition · group theory

MulHom.inverse

{M : Type u_4} →
  {N : Type u_5} →
    [inst : Mul M] →
      [inst_1 : Mul N] → (f : M →ₙ* N) → (g : N → M) → Function.LeftInverse g ⇑f → Function.RightInverse g ⇑f → N →ₙ* M

Makes a multiplicative inverse from a bijection which preserves multiplication.

Defined in
Mathlib.Algebra.Group.Hom.Defs
Cited by
3 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
MulMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MulEquiv.symm_map_mul · cited by 3MulEquiv.symm_map_mulMonoidHom.inverse · cited by 1MonoidHom.inverseNonUnitalRingHom.inverse · cited by 1NonUnitalRingHom.inverseRingHom.inverse · cited by 1RingHom.inverseNonUnitalAlgHom.inverse · cited by 1NonUnitalAlgHom.inverseNonUnitalAlgHom.inverse' · cited by 1NonUnitalAlgHom.inverse'MulHom.inverse.congr_simp · cited by 0inverse.congr_simpMulHom.inverse_apply · cited by 0MulHom.inverse_applyDFunLike.coe · cited by 62936DFunLike.coeMulHom · cited by 299MulHomMulHom.inverseCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • DFunLike.coestatement and proof · cited by 62,936
  • MulHomstatement and proof · cited by 299

Cited by8

Results whose statement or proof uses this declaration.