论文标题
posets的Koszul复合物和函子的相对同源代数
Koszul complexes and relative homological algebra of functors over posets
论文作者
论文摘要
在某些条件下，Koszul复合物可用于计算由POSET索引的矢量空间值函数的相对Betti图，而无需明确计算全局最小相对分辨率。在此类函子的相对同源代数中，自由函子被任意的函子代替。相对Betti图在最小的相对分辨率中编码这些函子的多重性。在本文中，我们提供了条件，在这些条件下，所选功能子家族的分级导致显式koszul络合物的同源尺寸为相对的betti图，从而为计算这些数值描述符的计算提供了方案。
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of global minimal relative resolutions. In relative homological algebra of such functors, free functors are replaced by an arbitrary family of functors. Relative Betti diagrams encode the multiplicities of these functors in minimal relative resolutions. In this article we provide conditions under which grading the chosen family of functors leads to explicit Koszul complexes whose homology dimensions are the relative Betti diagrams, thus giving a scheme for the computation of these numerical descriptors.
