Theorems · Definition · ring theory

Unitization.starLift

{R : Type u_1} →
  {A : Type u_2} →
    {C : Type u_3} →
      [inst : CommSemiring R] →
        [inst_1 : StarRing R] →
          [inst_2 : NonUnitalSemiring A] →
            [inst_3 : StarRing A] →
              [inst_4 : Module R A] →
                [inst_5 : SMulCommClass R A A] →
                  [inst_6 : IsScalarTower R A A] →
                    [inst_7 : Semiring C] →
                      [inst_8 : Algebra R C] →
                        [inst_9 : StarRing C] → [StarModule R C] → (A →⋆ₙₐ[R] C) ≃ (Unitization R A →⋆ₐ[R] C)

Non-unital star algebra homomorphisms from A into a unital star R-algebra C lift uniquely to Unitization R A →⋆ₐ[R] C. This is the universal property of the unitization.

Defined in

Mathlib.Algebra.Algebra.Unitization

Cited by

7 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringStarRingNonUnitalSemiringStarRingModuleSMulCommClassIsScalarTowerSemiringAlgebraStarRingStarModule