  We give an explicit description of the generator of finitely presented
objects of the coslice of a locally finitely presentable category under a given
object, as consisting of all pushouts of finitely presented maps under this
object. Then we prove that the comma category under the direct image part of a
morphism of locally finitely presentable category is still locally finitely
presentable, and we give again an explicit description of its generator of
finitely presented objects. We finally deduce that 2-category $\LFP$ has comma
objects computed in $\Cat$.
