2-Categorical Foundations for Multiparameter Persistence

Abstract: This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of traditional persistence modules. Our 2-categorical model yields new invariants that effectively characterize multidimensional topological features while maintaining computational tractability. We prove stability theorems for these invariants and demonstrate their effectiveness through applications in genomics and complex network analysis.