Locally Compact Objects in Exact Categories
We identify two categories of locally compact objects on an exact category A. They correspond to the wellknown 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 Ktheoretical 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/proobjects over any category C can be described as localizations of categories of diagrams over C.
Thu Nov 9 13:17:04 2017  permalink 

https://arxiv.org/abs/0710.2509v3