# Notes on Multiple Higher Category Theory

## TL;DR

This paper explores the application of the Stretchings method, originating from Globular Geometry, to develop algebraic models of weakened strict multiple higher categories and groupoids, advancing the understanding of weak higher categorical structures.

## Contribution

It adapts the Stretchings method to weakened strict multiple $
abla$-categories and constructs algebraic models of weak multiple $
abla$-groupoids, extending higher category theory techniques.

## Key findings

- Development of algebraic models for weak multiple $
abla$-categories
- Extension of Stretchings method to multiple $
abla$-categories
- Framework for modeling weak multiple $
abla$-groupoids

## Abstract

These notes follows the articles \cite{kamel, Cam, cam-cubique} which show how powerful can be the method of \textit{Stretchings} initiated with the \textit{Globular Geometry} by Jacques Penon in \cite{penon} , to weakened \textit{strict higher structures}. Here we adapt this method to weakened strict multiple $\infty$-categories, strict multiple $(\infty,m)$-categories, and in particular we obtain algebraic models of weak multiple $\infty$-groupoids.