  Given a diagram of small categories $F : J \rightarrow \textbf{Cat}$, we
provide a combinatorial description of its colimit in terms of the indexing
category $J$ and the categories and functors in the diagram $F$. We introduce
certain double categories of zig-zags in order to keep track of the necessary
identifications. We found these double categories necessary, but also
explanatory.
  When applied pointwise in the simplicially enriched setting, our
constructions offer a shorter proof of the necklace theorem of Dugger and
Spivak by direct computation.
