分层规范化下的图解基
Diagrammatic bases from stratified normalization
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中文总结 AI 辅助
本文提出一种基于分层重写系统的规范化方法，用于计算图解范畴的hom基，并应用于$q$-Schur范畴构造新基。
中文摘要 AI 辅助
在本文中，我们引入了一种新的重写方法，用于计算图解范畴的hom基。我们的方法基于分层表示，通过根据其关系的重写行为将等式表示划分为多个层来获得。我们建立了在环上具有系数的分层重写系统中终止性和合流性的模块化原理。然后，我们引入了一个完备化过程，将分层表示转换为规范化表示，其中连续层之间的混合相互作用被吸收到规范化的重写规则中，从而诱导合流性的模块化。这导致了图解范畴的分层hom基定理。我们通过将其应用于$q$-Schur范畴来说明该方法，并为其构造了一个新的hom基。
英文摘要
In this article, we introduce a new rewriting method for computing hom-bases of diagrammatic categories. Our approach is based on stratified presentations, obtained by partitioning an equational presentation into strata according to the rewriting behavior of its relations. We establish modularity principles for termination and confluence in stratified rewriting systems with coefficients in a ring. We then introduce a completion procedure that transforms a stratified presentation into a normalized one, in which mixed interactions between successive strata are absorbed into the normalized rewriting rules, thereby inducing modularity of confluence. This leads to a stratified hom-basis theorem for diagrammatic categories. We illustrate the method by applying it to the $q$-Schur category, for which we construct a new hom-basis.
