General Presentations of Algebras and Foundations of $\tau$-tilting Theory

TL;DR

This paper clarifies how key results in $ au$-tilting theory are derived from general algebra presentations, linking two significant areas in algebra research.

Contribution

It demonstrates that the main results of $ au$-tilting theory follow directly from existing results on general presentations of algebras, unifying these concepts.

Findings

Main results in $ au$-tilting theory follow from general algebra presentations.

Provides a unified perspective connecting $ au$-tilting theory with algebra presentations.

Simplifies understanding of $ au$-tilting results through existing algebraic frameworks.

Abstract

In this short note, we explain how the main results in "$\tau$-tilting theory" by Adachi-Iyama-Reiten follow from the results in Section 5 of "General presentations of algebras" by Derksen-Fei.