  In the efforts to define a 2-categorical analog of an abelian category, two
(or three) notions of "abelian 2-categories" are defined. One is the relatively
exact 2-category, and the other(s) is the (2-)abelian Gpd-category. We compare
these notions. Since they proceed independently in their own way, in different
settings and terminologies, it will be worth while to collect and unify them.
In this paper, by comparing their definitions and arguments, we show the
relationship among these classes of 2-categories.
