持续同调中的寿命函子与自然对偶性
Lifespan Functors and Natural Dualities in Persistent Homology
AI总结：
本文引入寿命函子，根据有界性过滤条形码区间，用于分类内射与投射对象，推广了持久（上）同调的对偶性结果，并为高效计算态射像、核与余核的条形码奠定基础。
摘要：
我们引入了寿命函子，这是持久性模块范畴上的自函子，可根据有界性属性从条形码中过滤区间。它们可用于对条形码范畴和逐点有限维持久性模块范畴中的内射对象和投射对象进行分类。它们也自然地出现在持久（上）同调的绝对和相对版本的对偶性结果中，推广了先前关于条形码的结果。由于它们的函子性，我们可以将这些结果应用于由过滤之间的态射诱导的持久同调中的态射。这为高效计算此类态射的像、核和余核的条形码奠定了基础。
英文摘要：
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.
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