论文标题
有限集的类固醇在钻机类别的2类中是生物元素
The groupoid of finite sets is biinitial in the 2-category of rig categories
论文作者
论文摘要
有限组的类固醇具有对称2-RIG的“规范”结构，其总和和产品分别由集合的相关和乘积给出。这个2 rig $ \ wideHat {\ mathbb {f} \ Mathbb {s} et} $只是交换性钻机$ \ mathbb {n} $自然数的众多非等效分类之一，与rig $ \ $ \ m m iance fir的类别一起列出了限制类别，该类别的类别，该类别的设置，整个类别，整个列表，整个组合列表，整个组合的整个类别在本文中，尺寸向量的空间在本文中表明，$ \ wideHat {\ sathbb {f} \ mathbb {s} et} $是$ \ mathbb {n} $的正确分类。钻机。作为副产品，从适当版本的$ \ wideHat {\ mathbb {f} \ mathbb {s} et} $中的任何（semistrict）$ \ mathbb {s} $中获得了$ \ mathbb {s} et} $的明确描述。 $ 1+\ stackrel {n）} {\ cdots}+1 $ in $ \ mathbb {s} $ in $ n \ geq 0 $。
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 $n\geq 0$.
