  Given a family of model categories $\cal E \to \cal C$, we associate to it a
homotopical category of derived, or Segal, sections $DSect(\cal C,\cal E)$ that
models the higher-categorical sections of the localisation $L\cal E \to \cal
C$. The derived sections provide an alternative, strict model for various
higher algebra objects appearing in the work of Lurie. We prove a few results
concerning the properties of the homotopical category $DSect(\cal C,\cal E)$,
and as an example, study its behaviour with respect to the base-change along a
select class of functors.
