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- W2024642776 abstract "The algebraic K -groups of an exact category M are defined by Quillen as K i M =л i+1 (Q M ) , i ≥0, where Q M is a category known as the Q -construction on M . For a ring R , K i P R = K i R (the usual algebraic K -groups of R ) where P R is the category of finitely generated projective right R -modules. Previous study of K ∗ R has required not only the Q construction, but also a model for the loop space of Q P R , known as the S −1 S -construction. Unfortunately, the S −1 S -construction does not yield a loop space for Q M when M is arbitrary. In this paper, two useful models of a loop space for Q M , with no restriction on the exact category M , are descibed. Moreover, these construction are shown to be directly related to the S −1 S -construction. The simpler of the two constructions fails to have a certain symmetry property with respect to dualization of the exact category M . This deficiency is eliminated in the second construction, which is somewhat more complicated. Applications are given to the relative algebraic K -theory of an exact functor of exact categories, with special attention given to the case when the exact functor is cofinal." @default.
- W2024642776 created "2016-06-24" @default.
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- W2024642776 date "1988-05-01" @default.
- W2024642776 modified "2023-10-16" @default.
- W2024642776 title "Loop spaces for the Q-construction" @default.
- W2024642776 cites W201935133 @default.
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- W2024642776 doi "https://doi.org/10.1016/0022-4049(88)90132-6" @default.
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