Lifespan functors and natural dualities in persistent homology
Lifespan functors and natural dualities in persistent homology
复制标题
持久同源中的寿命函子和自然对偶性
DOI：
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Maximilian Schmahl
中科院分区：
文献类型：
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作者：
Ulrich Bauer;Maximilian Schmahl
我们引入了寿命函子，它是持久性模块类别上的内函子，根据它们的有界性从条形码中过滤出间隔。它们可以用于对条形码类别和点向有限维持久模块类别中的射射和投影对象进行分类。它们也自然地出现在持久（co）同源的绝对和相对版本的对偶结果中，用条形码推广了以前的结果。由于它们的功能性，我们可以将这些结果应用于由过滤之间的态射引起的持久同构中的态射。这为有效地计算图像、核和此类态射的核的条形码奠定了基础。
We introduce lifespan functors, which are endofunctors on the category of persistence modules that filter out intervals from barcodes according to their boundedness properties. They can be used to classify injective and projective objects in the category of barcodes and the category of pointwise finite-dimensional persistence modules. They also naturally appear in duality results for absolute and relative versions of persistent (co)homology, generalizing previous results in terms of barcodes. Due to their functoriality, we can apply these results to morphisms in persistent homology that are induced by morphisms between filtrations. This lays the groundwork for the efficient computation of barcodes for images, kernels, and cokernels of such morphisms.
影响因子：
0.8
作者：
Torras-Casas Á
通讯作者：
Torras-Casas Á