论文标题
寿命函数和持续同源性的自然二元性
Lifespan Functors and Natural Dualities in Persistent Homology
论文作者
论文摘要
我们介绍了寿命函数，它们是持久模块类别的内型函数，可根据其有界性能从条形码中滤除间隔。它们可用于在条形码类别中对注射和投射对象进行分类，以及点式有限维持久性模块的类别。它们也自然出现在二元性结果中，用于持久性（CO）同源性的绝对和相对版本，从条形码方面概括了先前的结果。由于其功能性，我们可以将这些结果应用于持续的同源性中的形态，这些形态是由过滤之间的形态引起的。这为有效计算了这种形态的图像，内核和焦点的条形码有效地计算了基础。
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.
