Generalized Persistence Diagrams

Abstract: We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category. We call this the type A persistence diagram of a persistence module. If the category is also abelian, then we define a second type B persistence diagram. In addition, we show that both diagrams are stable to all sufficiently small perturbations of the module.