选择范畴与线性典范关系
Selective Categories and Linear Canonical Relations
摘要：
Wehrheim和Woodward的一个构造规避了光滑正则关系的组成并不总是光滑的问题，建立了一个适合函子量子化的范畴。为了将它们的构造应用到更多的例子中，我们引入了一个高选择范畴的概念，其中只有某些态射和这些态射中的某些对是“好的”。然后，我们将这个概念应用到范畴$\mathbf{SLREL}$的线性典型关系和结果${\rm WW}(\mathbf{SLREL})$的我们的版本的WW建设，确定在后者的态射对$(L,k)$组成的线性典型关系和非负整数。我们把这个类别的索引的线性典型关系的拓扑结构的组合是连续的，不同于$\mathbf{SLREL}$本身的组合。随后的论文将考虑这一类别从衍生几何的观点，并将关注量子同行。
英文摘要：
A construction of Wehrheim and Woodward circumvents the problem that compositions of smooth canonical relations are not always smooth, building a category suitable for functorial quantization. To apply their construction to more examples, we introduce a notion of highly selective category, in which only certain morphisms and certain pairs of these morphisms are "good". We then apply this notion to the category $\mathbf{SLREL}$ of linear canonical relations and the result ${\rm WW}(\mathbf{SLREL})$ of our version of the WW construction, identifying the morphisms in the latter with pairs $(L,k)$ consisting of a linear canonical relation and a nonnegative integer. We put a topology on this category of indexed linear canonical relations for which composition is continuous, unlike the composition in $\mathbf{SLREL}$ itself. Subsequent papers will consider this category from the viewpoint of derived geometry and will concern quantum counterparts.
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