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4 changes: 4 additions & 0 deletions Mathlib/RingTheory/TensorProduct/Pi.lean
Original file line number Diff line number Diff line change
Expand Up @@ -70,6 +70,10 @@ lemma piScalarRight_tmul_apply (x : A) (y : ι → R) (i : ι) :
piScalarRight R S A ι (x ⊗ₜ y) i = y i • x :=
rfl

theorem Algebra.TensorProduct.piScalarRight_symm_apply_algebraMap (x : ι → R) :
(piScalarRight R S A ι).symm (algebraMap _ _ x) = 1 ⊗ₜ[R] x := by
simp [AlgEquiv.symm_apply_eq, algebraMap_eq_smul_one, piScalarRight_tmul, Pi.smul_def']

section

variable (B C : Type*) [Semiring B] [Semiring C] [Algebra R B] [Algebra R C]
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