Theorems · Definition · ring theory

MonoidAlgebra.liftMagma

(R : Type u_1) →
  {A : Type u_4} →
    {M : Type u_7} →
      [inst : Semiring R] →
        [inst_1 : Mul M] →
          [inst_2 : NonUnitalNonAssocSemiring A] →
            [inst_3 : Module R A] →
              [IsScalarTower R A A] → [SMulCommClass R A A] → (M →ₙ* A) ≃ (MonoidAlgebra R M →ₙₐ[R] A)

The functor M ↦ R[M], from the category of magmas to the category of non-unital, non-associative algebras over R is adjoint to the forgetful functor in the other direction.

Defined in

Mathlib.Algebra.MonoidAlgebra.Basic

Cited by

2 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringMulNonUnitalNonAssocSemiringModuleIsScalarTowerSMulCommClass