二维配边上的双线性对与Deligne范畴的推广
Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category
摘要：
对称群的Deligne范畴是划分范畴的加法Karoubi闭包。当t为非负整数时，当t被可忽略态射的理想模化时，它产生对称群的表示范畴，而对于参数t的一般值，它是半单的.在Comes之后，划分范畴可以通过二维定向配边范畴的特定线性化来解释。Deligne范畴及其半单范畴也有类似的解释。这种观点与二维拓扑理论的普遍构造相结合，导致了分区和Deligne范畴的多参数monoidal推广，每个有理函数在一个变量中有一个。
英文摘要：
The Deligne category of symmetric groups is the additive Karoubi closure of the partition category. It is semisimple for generic values of the parameter t while producing categories of representations of the symmetric group when modded out by the ideal of negligible morphisms when t is a non-negative integer. The partition category may be interpreted, following Comes, via a particular linearization of the category of two-dimensional oriented cobordisms. The Deligne category and its semisimple quotients admit similar interpretations. This viewpoint coupled to the universal construction of two-dimensional topological theories leads to multi-parameter monoidal generalizations of the partition and the Deligne categories, one for each rational function in one variable.
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