Theorems · Definition

Equiv.algEquiv

(R : Type u_1) →
  {α : Type u_2} →
    {β : Type u_3} →
      [inst : CommSemiring R] →
        (e : α ≃ β) →
          [inst_1 : Semiring β] →
            [inst_2 : Algebra R β] →
              let semiring := e.semiring;
              have algebra := Equiv.algebra R e;
              α ≃ₐ[R] β

An equivalence e : α ≃ β gives an algebra equivalence α ≃ₐ[R] β where the R-algebra structure on α is the one obtained by transporting an R-algebra structure on β back along e.

Defined in

Mathlib.Algebra.Algebra.TransferInstance

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebra