An un-delooped version of algebraic K-theory

Gunnarsson T, Schwänzl R, Vogt RM, Waldhausen F (1992)
Journal of Pure and Applied Algebra 79(3): 255-270.

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Problems working with the Segal operations in algebraic K-theory of spaces—constructed by F. Waldhausen (1982)—arose from the absence of a nice groupcompletion on the category level. H. Grayson and D. Gillet (1987) introduced a combinatorial model G. for K-theory of exact categories. For dealing with K-theory of spaces we need an extension wG. of their result to the context of categories with cofibrations and weak equivalences. Our main result is that in the presence of a suspension functor—as in the case of retractive spaces—the wG. construction on the category of prespectra is an un-delooped version of the K-theory of the original category. In a sequel to this paper we show that Grayson's formula (1988) for Segal operations works as intended.
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Gunnarsson T, Schwänzl R, Vogt RM, Waldhausen F. An un-delooped version of algebraic K-theory. Journal of Pure and Applied Algebra. 1992;79(3):255-270.
Gunnarsson, T., Schwänzl, R., Vogt, R. M., & Waldhausen, F. (1992). An un-delooped version of algebraic K-theory. Journal of Pure and Applied Algebra, 79(3), 255-270.
Gunnarsson, T., Schwänzl, R., Vogt, R. M., and Waldhausen, F. (1992). An un-delooped version of algebraic K-theory. Journal of Pure and Applied Algebra 79, 255-270.
Gunnarsson, T., et al., 1992. An un-delooped version of algebraic K-theory. Journal of Pure and Applied Algebra, 79(3), p 255-270.
T. Gunnarsson, et al., “An un-delooped version of algebraic K-theory”, Journal of Pure and Applied Algebra, vol. 79, 1992, pp. 255-270.
Gunnarsson, T., Schwänzl, R., Vogt, R.M., Waldhausen, F.: An un-delooped version of algebraic K-theory. Journal of Pure and Applied Algebra. 79, 255-270 (1992).
Gunnarsson, T., Schwänzl, Roland, Vogt, R. M., and Waldhausen, Friedhelm. “An un-delooped version of algebraic K-theory”. Journal of Pure and Applied Algebra 79.3 (1992): 255-270.
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