Theorems · Definition · commutative algebra

Algebra.TensorProduct.includeLeft

{R : Type uR} →
  {S : Type uS} →
    {A : Type uA} →
      {B : Type uB} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : Algebra R A] →
              [inst_3 : Semiring B] →
                [inst_4 : Algebra R B] →
                  [inst_5 : CommSemiring S] →
                    [inst_6 : Algebra S A] → [inst_7 : SMulCommClass R S A] → A →ₐ[S] TensorProduct R A B

The R-algebra morphism A →ₐ[R] A ⊗[R] B sending a to a ⊗ₜ 1.

Defined in

Mathlib.RingTheory.TensorProduct.Basic

Cited by

72 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebraCommSemiringAlgebraSMulCommClass