论文标题
预示的相互作用分解
Interaction decomposition for presheaves
论文作者
论文摘要
考虑给定向量空间的向量子空间的集合以及这些向量空间上的投影仪集合，我们可以将矢量空间分解为矢量子空间的产物，从而使投影仪与投影同构一样吗？我们通过将交叉点属性与交互分解（在注射案例中完成）之间的关系扩展到投影案例，从而为这个问题提供了答案。这使我们能够对因子空间的相互作用分解。然后，我们将这些结果从poset扩展到了模块的类别，通过添加截面函数的数据存在。
Consider a collection of vector subspaces of a given vector space and a collection of projectors on these vector spaces, can we decompose the vector space into a product of vector subspaces such that the projectors are isomorphic to projections? We provide an answer to this question by extending the relation between the intersection property and the interaction decomposition (done in the injective case) to the projective case. This enables us to classify the decompositions of interactions for factor spaces. We then extend these results for presheaves from a poset to the category of modules by adding the data of a section functor when it exists.
