Theorems · Definition · ring theory

Unitization.lift

{R : Type u_2} →
  {A : Type u_3} →
    [inst : CommSemiring R] →
      [inst_1 : NonUnitalSemiring A] →
        [inst_2 : Module R A] →
          [inst_3 : SMulCommClass R A A] →
            [inst_4 : IsScalarTower R A A] →
              {C : Type u_5} → [inst_5 : Semiring C] → [inst_6 : Algebra R C] → (A →ₙₐ[R] C) ≃ (Unitization R A →ₐ[R] C)

Non-unital algebra homomorphisms from A into a unital 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

6 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringNonUnitalSemiringModuleSMulCommClassIsScalarTowerSemiringAlgebra