  The groupoid of finite sets has a "canonical" structure of a symmetric 2-rig
with the sum and product respectively given by the coproduct and product of
sets. This 2-rig $\widehat{\mathbb{F}\mathbb{S} et}$ is just one of the many
non-equivalent categorifications of the commutative rig $\mathbb{N}$ of natural
numbers, together with the rig $\mathbb{N}$ itself viewed as a discrete rig
category, the whole category of finite sets, the category of finite dimensional
vector spaces over a field $k$, etc. In this paper it is shown that
$\widehat{\mathbb{F}\mathbb{S} et}$ is the right categorification of
$\mathbb{N}$ in the sense that it is biinitial in the 2-category of rig
categories, in the same way as $\mathbb{N}$ is initial in the category of rigs.
As a by-product, an explicit description of the homomorphisms of rig categories
from a suitable version of $\widehat{\mathbb{F}\mathbb{S} et}$ into any
(semistrict) rig category $\mathbb{S}$ is obtained in terms of a sequence of
automorphisms of the objects $1+\stackrel{n)}{\cdots}+1$ in $\mathbb{S}$ for
each $n\geq 0$.
