Theorems · Definition · ring theory

SkewMonoidAlgebra.lift

(k : Type u_1) →
  (G : Type u_2) →
    [inst : CommSemiring k] →
      [inst_1 : Monoid G] →
        (A : Type u_4) →
          [inst_2 : Semiring A] →
            [inst_3 : Algebra k A] →
              [inst_4 : MulSemiringAction G k] →
                [inst_5 : SMulCommClass G k k] → (G →* A) ≃ (SkewMonoidAlgebra k G →ₐ[k] A)

Any monoid homomorphism G →* A can be lifted to an algebra homomorphism SkewMonoidAlgebra k G →ₐ[k] A.

Defined in

Mathlib.Algebra.SkewMonoidAlgebra.Lift

Cited by

7 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidSemiringAlgebraMulSemiringActionSMulCommClass