  We identify two categories of locally compact objects on an exact category A.
They correspond to the well-known constructions of the Beilinson category lim A
and the Kato category k(A). We study their mutual relations and compare the two
constructions. We prove that lim A is an exact category, which gives to this
category a very convenient feature when dealing with K-theoretical invariants.
It is natural therefore to consider the Beilinson category lim A as the most
convenient candidate to the role of the category of locally compact objects
over an exact category. We also show that the categories Ind_{aleph_0}(C),
Pro_{aleph_0}(C) of countably indexed ind/pro-objects over any category C can
be described as localizations of categories of diagrams over C.
