  Abstract inner automorphisms can be used to promote any category into a
2-category, and we study two-dimensional limits and colimits in the resulting
2-categories. Existing connected colimits and limits in the starting category
become two-dimensional colimits and limits under fairly general conditions.
Under the same conditions, colimits in the underlying category can be used to
build many notable two-dimensional colimits such as coequifiers and
coinserters. In contrast, disconnected colimits or genuinely 2-categorical
limits such as inserters and equifiers and cotensors cannot exist unless no
nontrivial abstract inner automorphisms exist and the resulting 2-category is
locally discrete. We also study briefly when an ordinary functor can be
extended to a 2-functor between the resulting 2-categories.
