论文标题
多项式函子的术语和衍生物通过否定
Terms and derivatives of polynomial functors via negation
论文作者
论文摘要
鉴于本地笛卡尔封闭的类别E，多项式（S，P，T）可以定义为一个图的图，该图由三个箭头组成。在本文中，我们定义了包含多项式（s，p，t）的均质和单一项，并在E上提供足够的条件，以便存在多项式的均匀术语。我们使用这些均匀术语来表现多项式和统一的多项式之间的无限型核置辅助家族。 我们表明，每个本地笛卡尔封闭的类别E具有严格的初始对象，均可允许否定操作员和（密集的，封闭的）正交分解系统。我们看到，多项式函数的术语和衍生物都是由该负算子构造的，并且如果人们通过密集的单态的W级将E定位，则所有多项式函数的衍生物都存在。 所有结果仅使用广泛的类别和分布性撤回理论正式显示。
Given a locally cartesian closed category E, a polynomial (s,p,t) may be defined as a diagram consisting of three arrows in E of a certain shape. In this paper we define the homogeneous and monomial terms comprising a polynomial (s,p,t) and give sufficient conditions on E such that the homogeneous terms of polynomials exist. We use these homogeneous terms to exhibit an infinite family of coreflection adjunctions between polynomials and homogeneous polynomials of order n. We show that every locally cartesian closed category E with a strict initial object admits a negation operator and a (dense,closed) orthogonal factorization system. We see that both terms and derivatives of polynomial functors are constructed from this negation operator, and that if one takes the localization of E by the class W of dense monomorphisms, then derivatives of all polynomial functors exist. All results are shown formally using only the theory of extensive categories and distributivity pullbacks.
