# Time-Varying Data as Sheaves: an Invitation to Narratives

arXiv: https://arxiv.org/abs/2609.09056 · HTML: https://mlsanity.com/paper/2609.09056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 58 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [Modern temporal network theory: A colloquium](https://mlsanity.com/paper/1508.01303/) (2015)
- [An Introduction to Temporal Graphs: An Algorithmic Perspective](https://mlsanity.com/paper/1503.00278/) (2015)
- [Distributed Multi-agent Coordination over Cellular Sheaves](https://mlsanity.com/paper/2504.02049/) (2025)
- [Heterogeneous Multi-Agent Multi-Target Tracking using Cellular Sheaves](https://mlsanity.com/paper/2512.24886/) (2025)
- [Towards a Unified Theory of Time-Varying Data](https://mlsanity.com/paper/2402.00206/) (2024)
- [Hierarchical Control of Multi-Agent Systems using Online Reinforcement Learning](https://mlsanity.com/paper/2007.14186/) (2020)
- [Diachronic Data Analysis Supports and Refines Conceptual Metaphor Theory](https://mlsanity.com/paper/2209.12234/) (2022)

## Abstract (arXiv)

Modern science and engineering increasingly rely on time-varying data, yet the mathematical tools used to model temporal phenomena are often developed within separate disciplines, obscuring common principles and limiting the transfer of ideas across fields. This chapter presents the theory of narratives, an abstract framework for time-varying objects of any mathematical kind that supports both theoretical investigations and applications. To illustrate this perspective, the chapter develops three vignettes, each illustrating a different research direction. The first addresses a general concern: What information loss can occur when switching between different representations of temporal data? The second concerns structural and algorithmic approaches: How can we systematically decompose time-varying data into simple pieces and obtain invariants describing its structural complexity? The third is an application to control theory: How can we model multi-agent systems with switching communication topologies? More important than any individual vignette, the central message of this invitation is that a suitable abstract perspective can organize and guide research across remarkably diverse mathematical and scientific domains.