  Among cocomplete categories, the locally presentable ones can be defined as
those with a strong generator consisting of presentable objects. Assuming
Vop{\v{e}}nka's Principle, we prove that a cocomplete category is locally
presentable iff it has a colimit dense subcategory and a generator consisting
of presentable objects. We further show that a $3$-element set is colimit-dense
in $\Set^{\op}$, and spaces of countable dimension are colimit-dense in
$\Vec^{op}$.
