Algebraic stability theorem for derived categories of zigzag persistence modules.
We study distances on zigzag persistence modules from the viewpoint of derived categories. It is known that the derived categories of ordinary and arbitrary zigzag persistence modules are equivalent. Through this derived equivalence, we define distances on the derived category of arbitrary zigzag persistence modules and prove an algebraic stability theorem. We also compare our distance with the distance for purely zigzag persistence modules introduced by Botnan--Lesnick and the sheaf-theoretic convolution distance due to Kashiwara--Schapira.