A short proof of HRS-tilting

TL;DR

This paper provides a concise proof of the Happel-Reiten-Smal{ exto} tilting theorem, establishing derived equivalence between abelian categories connected by tilting, through an explicit construction.

Contribution

It offers a shorter, more direct proof of the HRS-tilting theorem using explicit construction methods.

Findings

Proves derived equivalence between abelian categories linked by tilting.

Provides an explicit construction method for the proof.

Simplifies the understanding of the HRS-tilting theorem.

Abstract

We give a short proof to the following tilting theorem by Happel, Reiten and Smal{\o} via an explicit construction: given two abelian categories $\mathcal{A}$ and $\mathcal{B}$ such that $\mathcal{B}$ is tilted from $\mathcal{A}$, then $\mathcal{A}$ and $\mathcal{B}$ are derived equivalent.