# UnivariatePolynomialCategoryFunctions2(R, PR, S, PS)ΒΆ

- R: Join(SemiRng, AbelianMonoid)
- PR: UnivariatePolynomialCategory R
- S: Join(SemiRng, AbelianMonoid)
- PS: UnivariatePolynomialCategory S

Mapping from polynomials over `R`

to polynomials over `S`

given a map from `R`

to `S`

assumed to send zero to zero.

- map: (R -> S, PR) -> PS
`map(f, p)`

takes a function`f`

from`R`

to`S`

, and applies it to each (non-zero) coefficient of a polynomial`p`

over`R`

, getting a new polynomial over`S`

. Note: since the map is not applied to zero elements, it may map zero to zero.