Mitchell's embedding theorem

Let \(\mathcal{A}\) be small abelian category. Then there exists a ring \(R\) and a fully faithful exact functor

\begin{align*} \mathcal{F}: \mathcal{A} \rightarrow \mathrm{RMod} \end{align*}

for the category RMod for some ring \(R\)

see also full conservative functor and isomorphic objects ; diagram chasing in an abelian category