Theorems · Definition · ring theory

IsSymmetricAlgebra.lift

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {A : Type u_3} →
            [inst_3 : CommSemiring A] →
              [inst_4 : Algebra R A] →
                {f : M →ₗ[R] A} →
                  IsSymmetricAlgebra f →
                    {A' : Type u_4} → [inst_5 : CommSemiring A'] → [inst_6 : Algebra R A'] → (M →ₗ[R] A') → A →ₐ[R] A'

Given a morphism g : M →ₗ[R] A', lift this to a morphism of type A →ₐ[R] A' (where A satisfies the universal property of the symmetric algebra of M)

Defined in

Mathlib.LinearAlgebra.SymmetricAlgebra.Basic

Cited by

4 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAlgebraCommSemiringAlgebra