当博弈比较成为博弈：绝对的对策论
When game comparison becomes play: Absolutely Categorical Game Theory
摘要：
组合博弈的绝对宇宙，正如同一作者在最近的一篇论文中所定义的，包括许多标准的短正规- misère-和scoring-play幺半群。在本说明中，我们表明，类是分类的，通过扩展Joyal的建设正常发挥游戏中的箭头。给定$G$和$H$在一个绝对宇宙$U$中，我们研究了左预备赛$[G, H]$，这是一个正常的游戏，独立于特定的绝对宇宙，并发现$G\longrightarrow H$（暗示$G\succcurlyeq H$）对应于一组获胜策略，左第二次在$[G,H]$。由此我们定义了范畴${\bf LNP(U)}$。
英文摘要：
Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- misère- and scoring-play monoids. In this note we show that the class is categorical, by extending Joyal's construction of arrows in normal-play games. Given $G$ and $H$ in an Absolute Universe $U$, we study instead the Left Provisonal Game $[G, H]$, which is a normal-play game, independently of the particular Absolute Universe, and find that $G\longrightarrow H$ (implying $G\succcurlyeq H$) corresponds to the set of winning strategies for Left playing second in $[G,H]$. By this we define the category ${\bf LNP(U)}$.
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