We provide a definition of ephemeral multipersistent modules and prove that the quotient category of persistent modules by the ephemeral ones is equivalent to the category of –sheaves. In the case of one-dimensional persistence, our definition agrees with the usual one, showing that the observable category and the category of –sheaves are equivalent. We also establish isometry theorems between the category of persistent modules and –sheaves both endowed with their interleaving distance. Finally, we compare the interleaving and convolution distances.
"Ephemeral persistence modules and distance comparison." Algebr. Geom. Topol. 21 (1) 247 - 277, 2021. https://doi.org/10.2140/agt.2021.21.247