  In this paper, we obtain a non-abelian analogue of Lubkin's embedding theorem
for abelian categories. Our theorem faithfully embeds any small regular
Mal'tsev category $\mathbb{C}$ in an $n$-th power of a particular locally
finitely presentable regular Mal'tsev category. The embedding preserves and
reflects finite limits, isomorphisms and regular epimorphisms, as in the case
of Barr's embedding theorem for regular categories. Furthermore, we show that
we can take $n$ to be the (cardinal) number of subobjects of the terminal
object in $\mathbb{C}$.
