# Higher Morse moduli spaces and n-categories

## TL;DR

This paper extends the concept of flow categories in Morse theory to an almost strict n-category framework by iteratively applying Morse theory on Morse moduli spaces, introducing a new categorical structure.

## Contribution

It constructs an almost strict n-category from Morse moduli spaces, generalizing previous flow categories to higher categorical levels.

## Key findings

- Established an almost strict n-category structure
- Developed suitable Morse functions for higher moduli spaces
- Demonstrated the categorical framework's consistency

## Abstract

We generalize Cohen & Jones & Segal's flow category whose objects are the critical points of a Morse function and whose morphisms are the Morse moduli spaces between the critical points to an n-category. The n-category construction involves repeatedly doing Morse theory on Morse moduli spaces for which we have to construct a class of suitable Morse functions. It turns out to be an `almost strict' n-category, i.e. it is a strict n-category `up to canonical isomorphisms'.