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The groupoid of finite sets has a "canonical" structure of a symmetric 2-rigwith the sum and product respectively given by the coproduct and product ofsets. This 2-rig $\widehat{\mathbb{F}\mathbb{S} et}$ is just one of the manynon-equivalent categorifications of the commutative rig $\mathbb{N}$ of naturalnumbers, together with the rig $\mathbb{N}$ itself viewed as a discrete rigcategory, the whole category of finite sets, the category of finite dimensionalvector 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 rigcategories, 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 categoriesfrom a suitable version of $\widehat{\mathbb{F}\mathbb{S} et}$ into any(semistrict) rig category $\mathbb{S}$ is obtained in terms of a sequence ofautomorphisms of the objects $1+\stackrel{n)}{\cdots}+1$ in $\mathbb{S}$ foreach $n\geq 0$.

The groupoid of finite sets is biinitial in the 2-category of rig categories