Let $R$ be a commutative ring and $R[X_1,...,X_n]^{S_n}$ be the ring of symmetric polynomials.
I have learned some basic properties of this ring and the results are really similar to those by symmetric tensors. (E.g. Formula for the natural generators of the ring of symmetric formulas is exactly the same as the natural $R$-basis for $n$-th symmetric power of a module)
Not vieweing these two differently, what would be a viewpoint to see these things in one way? Or do the rings of symmetric polynomials form a subcategory of symmetric algebras?