论文标题
最终的图像
The eventual image
论文作者
论文摘要
在具有足够限制和colimits的类别中，可以在两种双重感觉中形成内态的普遍自动形态。有时，这些双重构造的重合，例如有限组，有限维矢量空间和紧凑的度量空间的类别。从那里开始，从内态$ f $开始，$ f $上有一个双倍的自动形态，其基础对象是最终的图像$ \ bigCap_n \ mathrm {im}（im}（f^n）$。我们的主要定理统一了这些示例，并指出，在满足某些公理的任何类别化系统中，最终图像具有两个双通用属性。进一步的定理将最终的图像描述为末端山地。总共给出了最终图像的九个特征，在不同级别的一般性上有效。
In a category with enough limits and colimits, one can form the universal automorphism on an endomorphism in two dual senses. Sometimes these dual constructions coincide, as in the categories of finite sets, finite-dimensional vector spaces, and compact metric spaces. There, beginning with an endomorphism $f$, there is a doubly-universal automorphism on $f$ whose underlying object is the eventual image $\bigcap_n \mathrm{im}(f^n)$. Our main theorem unifies these examples, stating that in any category with a factorization system satisfying certain axioms, the eventual image has two dual universal properties. A further theorem characterizes the eventual image as a terminal coalgebra. In all, nine characterizations of the eventual image are given, valid at different levels of generality.
