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    Locally Compact Objects in Exact Categories

    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_{aleph0}(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.

    November 9, 2017 at 1:17:04 PM GMT - permalink -
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    - https://arxiv.org/abs/0710.2509v3
    math ind pro LFP3
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