A short proof of HRS-tilting

We give a short proof to the following tilting theorem by Happel, Reiten and Smalø 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.

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