We introduce integral structure types as a categorical analogue of virtual combinatorial species. Integral structure types then categorify power series with possibly negative coefficients in the same way that combinatorial species categorify power series with non-negative rational coefficients. The notion of an operator on combinatorial species naturally extends to integral structure types, and in light of their ‘negativity’ we define the notion of the commutator of two operators on integral structure types. We then extend integral structure types to the setting of stuff types as introduced by Baez and Dolan, and then conclude by using integral structure types to give a combinatorial description for Chern classes of projective hypersurfaces.

中文翻译：

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论整体结构类型

我们引入积分结构类型作为虚拟组合物种的分类类似物。积分结构类型然后以与组合物种分类具有非负有理系数的幂级数相同的方式将幂级数分类为可能具有负系数的幂级数。组合物种上的运算符的概念自然扩展到积分结构类型，并且鉴于它们的“负性”，我们定义了积分结构类型上的两个运算符的交换子的概念。然后我们将积分结构类型扩展到 Baez 和 Dolan 介绍的东西类型的设置，然后通过使用积分结构类型给出对射影超曲面的陈类的组合描述。