  Symmetric powers are an important notion in mathematics, computer science and
physics. In mathematics, they are used to build symmetric algebras, in computer
science, to build free exponential modalities of linear logic and in physics,
Fock spaces. We study symmetric powers through the lens of category theory. We
focus here on the simpler case where nonnegative rational scalars are available
ie. we study symmetric powers in symmetric monoidal $\mathbb{Q}_{\ge 0}$-linear
categories. Among the developments, a main point is the introduction of the
notion of binomial graded bimonoid and the associated string diagrams which
characterize symmetric powers in this setting.
