The Freyd-Mitchell's embedding theorem asserts that if $\mathcal{C}$ is a small abelian category, then there exists a ring $R$ and a fully faithful, exact functor $F$ from $\mathcal{C}$ to the category of left modules over $R$.
My question here is that: Do we really need $\mathcal{C}$ to be a small category? I am a little bit confused since the Wikipedia page includes smallness in the statement of the theorem, while Ravi Vakil, in his Foundations of Algebraic Geometry note (section 1.6.4), only requires $\mathcal{C}$ to be a locally small abelian category.