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 $n\ge 0$.

有限集的类群具有对称2-rig的“规范”结构，其总和和乘积分别由集合的协积和乘积给出。这个2钻机$\widehat{\mathbb{F}\mathbb{小号}ËŤ}$ 只是换向钻机的许多非等价分类之一 $\mathbb{ñ}$ 的自然数，以及装备 $\mathbb{ñ}$本身被视为离散钻机类别，有限集的整个类别，字段k上的有限维向量空间的类别，等等。$\widehat{\mathbb{F}\mathbb{小号}ËŤ}$ 是...的正确分类 $\mathbb{ñ}$ 从某种意义上说，它在钻机类别的2类中是二项式的，与 $\mathbb{ñ}$在钻机类别中是最初的。作为副产品，从合适版本的钻机类别中明确描述了钻机类别的同态性$\widehat{\mathbb{F}\mathbb{小号}ËŤ}$ 属于任何（半）钻机类别 $\mathbb{小号}$ 是根据对象的自同构序列获得的 $\mathrm{1个}+\stackrel{ñ）}{\cdots }+\mathrm{1个}$ 在 $\mathbb{小号}$ 对于每个 $ñ\ge 0$。