English
There is an R-algebra homomorphism from U.restrictScalars R to B induced by an S-algebra homomorphism from U, i.e., a restriction-of-scalars map along the tower.
Русский
Существует R-алгебра гомоморфизм от U.restrictScalars R к B, индуцированный S-алгебра гомоморфизмом от U.
LaTeX
$$$\text{ofRestrictScalars}(U,f) : U.restrictScalars R \to_B B$$$
Lean4
/-- Produces an `R`-algebra map from `U.restrictScalars R` given an `S`-algebra map from `U`.
This is a special case of `AlgHom.restrictScalars` that can be helpful in elaboration. -/
@[simp]
def ofRestrictScalars (U : Subalgebra S A) (f : U →ₐ[S] B) : U.restrictScalars R →ₐ[R] B :=
f.restrictScalars R