# A geometric perspective on the $\tau$-cluster morphism category

## TL;DR

This paper introduces a geometric approach to understanding the $ au$-cluster morphism category using wall-and-chamber structures, simplifying its definition and proof of well-definedness.

## Contribution

It provides a novel geometric perspective on the $ au$-cluster morphism category, making its properties easier to establish.

## Key findings

- The $ au$-cluster morphism category can be characterized via wall-and-chamber structures.
- The geometric perspective simplifies the proof of the category being well-defined.
- The approach enhances understanding of the category's structure in algebra.

## Abstract

We show how the $\tau$-cluster morphism category may be defined in terms of the wall-and-chamber structure of an algebra. This geometric perspective leads to a simplified proof that the category is well-defined.