  We establish two versions of a central theorem, the Family Colimit Theorem,
for the coarse coherence property of metric spaces. This is a coarse geometric
property and so is well-defined for finitely generated groups with word
metrics. It is known that coarse coherence of the fundamental group has
important implications for classification of high-dimensional manifolds. The
Family Colimit Theorem is one of the permanence theorems that give structure to
the class of coarsely coherent groups. In fact, all known permanence theorems
follow from the Family Colimit Theorem. We also use this theorem to construct
new groups from this class.
