The General Adjoint Functor Theorem (Category Theory) states that for a locally small and complete category $D$, a functor $G\colon D \to C$ has a left adjoint if and only if $G$ preserves all small limits and for each object $A$ in $C$, $A \downarrow G$) has a weakly initial set.
Could someone help by giving an example of a functor $G$ that preserves all small limits but has no left adjoint?