Proposition 6.8. Assuming that:

$C$ a small category
$C$ has finite limits
$F : C \to S e t$ a functor

Then the following are equivalent:

(i)
$F$ preserves finite limits.
(ii)
$(1 ↓ F)$ is cofiltered.
(iii)
$F$ is expresible as a filtered colimit of representable functors.