Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifespan Functors and Natural Dualities in Persistent Homology   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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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph