Geodesic
Lifespan functors and natural dualities in persistent homology
Homology, homotopy, and applications, Tome 25 (2023) no. 2, pp. 297-327.

Voir la notice de l'article provenant de la source International Press of Boston

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 co-kernels of such morphisms.
DOI : 10.4310/HHA.2023.v25.n2.a13
Classification : 16G20, 18G05, 55U10, 57N15
Keywords: barcode, persistent homology, duality, injectivity, projectivity 
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     title = {Lifespan functors and natural dualities in persistent homology},
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     pages = {297--327},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a13/}
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Ulrich Bauer; Maximilian Schmahl. Lifespan functors and natural dualities in persistent homology. Homology, homotopy, and applications, Tome 25 (2023) no. 2, pp. 297-327. doi : 10.4310/HHA.2023.v25.n2.a13. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2023.v25.n2.a13/

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