2-Categorical Foundations for Multiparameter Persistence

TL;DR

This paper presents a 2-categorical framework for multi-parameter persistence, enabling better characterization of multidimensional topological features with stable invariants and practical applications in genomics and network analysis.

Contribution

It introduces a novel 2-categorical approach to multiparameter persistence, overcoming limitations of traditional methods and providing new stable invariants.

Findings

New 2-categorical invariants effectively characterize multidimensional features.

Framework maintains computational tractability for complex data.

Applications demonstrate practical utility in genomics and network analysis.

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.