On $\tau$-tilting theory

TL;DR

This paper introduces $ au$-tilting theory, a unifying framework that connects silting and cluster tilting theories, highlighting its historical development and recent advances.

Contribution

It provides a concise overview of $ au$-tilting theory, emphasizing its role in unifying different tilting theories and summarizing recent progress.

Findings

Unifies silting and cluster tilting theories

Provides historical context and recent developments in $ au$-tilting theory

Serves as an introductory overview of the field

Abstract

We give a brief introduction to $\tau$-tilting theory [AIR]. In particular, we will see how our theory unifies two different branches of tilting theory, namely, silting theory and cluster tilting theory. We also introduce the history and recent developments.