Journal of Pure and Applied Algebra ( IF 0.7 ) Pub Date : 2021-03-15 , DOI: 10.1016/j.jpaa.2021.106738 Josep Elgueta
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 is just one of the many non-equivalent categorifications of the commutative rig of natural numbers, together with the rig 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 is the right categorification of in the sense that it is biinitial in the 2-category of rig categories, in the same way as 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 into any (semistrict) rig category is obtained in terms of a sequence of automorphisms of the objects in for each .
中文翻译:
有限集的类群在钻机类别的2类中是双初始的
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 只是换向钻机的许多非等价分类之一 的自然数,以及装备 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。 是...的正确分类 从某种意义上说,它在钻机类别的2类中是二项式的,与 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 属于任何(半)钻机类别 是根据对象的自同构序列获得的 在 对于每个 。