AI 中文总结
受代数对应和线性算子启发引入拟阵对应及其多拟阵类似物，定义函子产生多种标准函子，证明其在自然假设下保持相关性质，建立与多重对称提升的兼容性并联系线性算子支撑。
AI 中文摘要
受与体积和洛伦兹多项式相关的代数对应和线性算子的启发，我们引入了拟阵对应及其多拟阵类似物。拟阵对应定义了一个在拟阵偏序范畴之间的函子，其态射是拟阵商，各种标准函子，包括删除、收缩、自由扩张、截断、交、并和拉回，都以这种方式产生。我们表明，在自然假设下，这些对应保持可表示性和代数性。在多拟阵设置中，我们建立了与多重对称提升的兼容性。最后，我们将此构造与具有洛伦兹符号的线性算子的支撑联系起来。
英文摘要
Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues. A matroid correspondence defines a functor between poset categories of matroids whose morphisms are matroid quotients, and various standard functors, including deletion, contraction, free extension, truncation, intersection, union, and pullback, arise in this way. We show that these correspondences preserve representability and algebraicity under natural hypotheses. In the polymatroid setting, we establish compatibility with multisymmetric lifts. Finally, we relate this construction to the supports of linear operators with Lorentzian symbols.
