论文标题
分类符号几何形状的功能性
Functoriality in categorical symplectic geometry
论文作者
论文摘要
分类符号几何形状是对符号歧管的丰富集合的研究，包括福卡亚$ a_ \ a_ \ infty $ - 类别，浮子共同体和符号共同体学。从2000年代后期的Wehrheim和Woodward的作品开始，几位作者开发了用于操纵这些不变的技术。我们调查了这些功能结构，包括Wehrheim-Woodward的quil缝浮子的共同体和与拉格朗日通讯相关的函子，福卡亚的替代方法可以定义福卡亚$ a_ \ a_ \ iftty $类别之间的函数，以及第二作者正在进行的Symplectic $（A__ \ Iffty，2类）的持续构建。在最后一部分中，我们描述了此思想圈的许多直接和间接应用，并在福卡亚$ a_ \ infty $ -scategory的背景下提出了Barr-Beck Monadicity标准的猜想版本。
Categorical symplectic geometry is the study of a rich collection of invariants of symplectic manifolds, including the Fukaya $A_\infty$-category, Floer cohomology, and symplectic cohomology. Beginning with work of Wehrheim and Woodward in the late 2000s, several authors have developed techniques for functorial manipulation of these invariants. We survey these functorial structures, including Wehrheim-Woodward's quilted Floer cohomology and functors associated to Lagrangian correspondences, Fukaya's alternate approach to defining functors between Fukaya $A_\infty$-categories, and the second author's ongoing construction of the symplectic $(A_\infty,2)$-category. In the last section, we describe a number of direct and indirect applications of this circle of ideas, and propose a conjectural version of the Barr-Beck Monadicity Criterion in the context of the Fukaya $A_\infty$-category.
