Deligne插值范畴的Khovanov-Sazdanovic推广中的不可分解对象
Indecomposable objects in Khovanov-Sazdanovic's generalizations of Deligne's interpolation categories
AI总结：
该研究针对Khovanov-Sazdanovic提出的Deligne插值范畴的推广形式，通过引入带滤过Krull-Schmidt范畴的相伴分次范畴等工具，完成了不可分解对象的分类并确定了相伴分次Grothendieck环。
摘要：
Khovanov与Sazdanovic近期引入了由有理函数参数化、通过二维配边范畴的商给出的对称幺半范畴，这些范畴推广了对称群表示的Deligne插值范畴。本文通过一般域上多项式环的交叉积对应的表示范畴之和，对Khovanov-Sazdanovic范畴的不可分解对象进行了分类，并确定了其相伴分次Grothendieck环。为得到这些结果，我们为带滤过的Krull-Schmidt范畴引入了相伴分次范畴，作为相伴分次Grothendieck环的范畴化，并研究了Krull-Schmidt范畴的域扩张与Galois下降理论。
英文摘要：
Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categories generalize Deligne's interpolation categories of representations of symmetric groups. In this paper, we classify indecomposable objects and identify the associated graded Grothendieck rings of Khovanov-Sazdanovic's categories through sums of representation categories over crossed products of polynomial rings over a general field. To obtain these results, we introduce associated graded categories for Krull-Schmidt categories with filtrations as a categorification of the associated graded Grothendieck ring, and study field extensions and Galois descent for Krull-Schmidt categories.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
