Theorems · Definition · nonassociative algebras

NonUnitalAlgHom.restrictScalars

(R : Type u_1) →
  {S : Type u_2} →
    {A : Type u_3} →
      {B : Type u_4} →
        [inst : Monoid R] →
          [inst_1 : Monoid S] →
            [inst_2 : NonUnitalNonAssocSemiring A] →
              [inst_3 : NonUnitalNonAssocSemiring B] →
                [inst_4 : MulAction R S] →
                  [inst_5 : DistribMulAction S A] →
                    [inst_6 : DistribMulAction S B] →
                      [inst_7 : DistribMulAction R A] →
                        [inst_8 : DistribMulAction R B] →
                          [IsScalarTower R S A] → [IsScalarTower R S B] → (A →ₙₐ[S] B) → A →ₙₐ[R] B

If a monoid R acts on another monoid S, then a non-unital algebra homomorphism over S can be viewed as a non-unital algebra homomorphism over R.

Defined in

Mathlib.Algebra.Algebra.NonUnitalHom

Cited by

4 results in Mathlib

Foundations

Depth 22 from the axioms · uses no axioms

Assumes

MonoidMonoidNonUnitalNonAssocSemiringNonUnitalNonAssocSemiringMulActionDistribMulActionDistribMulActionDistribMulActionDistribMulActionIsScalarTowerIsScalarTower