Algebraic structures on the target "Y" are inherited by the set of germs with values in "Y". For instance, if the target "Y" is a group, then it makes sense to multiply germs: to define ["f"]"x"["g"]"x", first take representatives "f" and "g", defined on neighbourhoods "U" and "V" respectively, and define ["f"]"x"["g"]"x" to be the germ at "x" of the pointwise product map "fg" (which is defined on formula_13). In the same way, if "Y" is an abelian group, vector space, or ring, then so is the set of germs.