Variant 9.2.3.9 (Lazard's Theorem). Let $R$ be an associative ring. Recall that a (left) $R$-module $M$ is flat if the tensor product functor
\[ \{ \textnormal{Right $R$-modules} \} \xrightarrow { \otimes _{R} M} \{ \textnormal{Abelian Groups} \} \]
is exact. It is easy to see that the collection of flat $R$-modules is closed under the formation of filtered colimits. Conversely, a theorem of Lazard ([MR0168625]) asserts that every flat $R$-module $M$ can be realized as a filtered colimit of free $R$-modules of finite rank (see 
for a more general statement). It follows that the category of flat $R$-modules is an $\operatorname{Ind}$-completion of the full subcategory spanned by the free $R$-modules of finite rank.