论文标题
交织和匹配作为表示
Interleavings and Matchings as Representations
论文作者
论文摘要
为了更好地理解和比较持久模块之间的交织，我们详细阐述了一般环境中交织的代数结构。特别是，我们为交织提供了一个表示理论框架，表明固定翻译下的交织类别与我们所谓的鞋带的表示类别是同构的。使用我们的框架，我们表明同一对持久模块的任何两个交织本身都是交错的。此外，在$ \ mathbb {z} $上的持久性模块的特殊情况下，我们表明条形码之间的匹配对应于间隔可分配的交织。
In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, showing that the category of interleavings under a fixed translation is isomorphic to the representation category of what we call a shoelace. Using our framework, we show that any two interleavings of the same pair of persistence modules are themselves interleaved. Furthermore, in the special case of persistence modules over $\mathbb{Z}$, we show that matchings between barcodes correspond to the interval-decomposable interleavings.
