Suppose $C$ is a cocomplete category with initial object $I$ and terminal object $T\neq I$.
The forgetful functor $U:T/C\to C$ does not preserve colimits, because the empty colimit in the under category $T/C$ is its initial object $T$ and the empty colimit in $C$ is $I$.
My impression is that these are ''the only'' non-preserved colimits. Is this true? If not, does $U$ at least preserve pushouts?