  We study locally constant coefficients. We first study the theory of homotopy
Kan extensions with locally constant coefficients in model categories, and
explain how it characterizes the homotopy theory of small categories. We
explain how to interpret this in terms of left Bousfield localization of
categories of diagrams with values in a combinatorial model category. At last,
we explain how the theory of homotopy Kan extensions in derivators can be used
to understand locally constant functors.
