A well known result states that, if $F:C \rightarrow D$ is a covariant functor between categories which admit finite projective limits, then $F$ is left exact if and only if it preserves finite projective limits.
I need to use this result, but unfortunately I was unable to find a reference or to prove it by myself. I would like to have one of the two.
Note: For completeness it's useful to say that the same result holds for right exact functor and finite direct limits. And that a functor preserves finite projective limits if and only if it preserves final objects and fiber products, or if and only if it preserves final objects, products and equalizers.
Edit: The definition of left exactness I suppose given is the one that can be found in wikipedia: http://en.wikipedia.org/wiki/Exact_functor. Which is: "$F$ is left exact if it brings the short exact sequence $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ of objects (and morphisms) of $C$ to an exact sequence $0 \rightarrow F(A) \rightarrow F(B) \rightarrow F(C) \rightarrow ...$ of objects of $D$". I don't think the result is untrue since also the page I linked states the result.