Abstract
We define notions of direct and inverse limits in an
n
-category. We prove that the
n+1
-category
nCA
T
′
of fibrant
n
-categories admits direct and inverse limits. At the end we speculate (without proofs) on some applications of the notion of limit, including homotopy fiber product and homotopy coproduct for
n
-categories, the notion of
n
-stack, representable functors, and finally on a somewhat different note, a notion of relative Malcev completion of the higher homotopy at a representation of the fundamental group.