Gunnarsson, T.; Schwänzl, R.; Vogt, R. M.; Waldhausen, F. An un-delooped version of algebraic \(K\)-theory. (English) Zbl 0757.19003 J. Pure Appl. Algebra 79, No. 3, 255-270 (1992). This paper extends the construction, by Gillet and Grayson, of a combinatorial model \(G_ \bullet\) for the \(K\)-theory of exact categories in the sense of Quillen, to the context of categories with cofibrations and weak equivalences. The main result is that in the presence of a suspension functor, the extended \(wG_ \bullet\) construction on the category of prespectra is an undelooped version of the \(K\)-theory of the original category. These constructions allow the definition and proofs of formulas for \(\lambda-\) and Segal operations in the algebraic \(K\)-theory of spaces. Reviewer: M.R.Stein (Evanston) Cited in 4 Documents MSC: 19D10 Algebraic \(K\)-theory of spaces 55N15 Topological \(K\)-theory 18E10 Abelian categories, Grothendieck categories Keywords:Segal operations; combinatorial model; categories with cofibrations and weak equivalences; suspension functor; category of prespectra; algebraic \(K\)-theory of spaces PDFBibTeX XMLCite \textit{T. Gunnarsson} et al., J. Pure Appl. Algebra 79, No. 3, 255--270 (1992; Zbl 0757.19003) Full Text: DOI References: [1] Bousfield, A. K.; Kan, D. M., Homotopy Limits, Completions and Localizations, (Lecture Notes in Mathematics, 304 (1972), Springer: Springer Berlin), (2nd corrected printing: 1987). · Zbl 0259.55004 [2] Gillet, H.; Grayson, D., The loop space of the \(Q\)-construction, Illinois J. Math., 31, 574-597 (1987) · Zbl 0628.55011 [3] Grayson, D., Exact sequences in algebraic \(K\)-theory, Illinois J. Math., 31, 598-617 (1987) · Zbl 0629.18010 [4] Grayson, D. R., Exterior power operations on higher \(K\)-theory (1988), Preprint [5] Gunnarsson, T., Abstract Homotopy Theory and Related Topics, Thesis (1978), Gothenburg [6] T. Gunnarsson and R. Schwänzl, Operations in \(A\); T. Gunnarsson and R. Schwänzl, Operations in \(A\) [7] Quillen, D., Higher Algebraic \(K\)-theory I, (Lecture Notes in Mathematics, 341 (1973), Springer: Springer Berlin) · Zbl 1198.19001 [8] Segal, G., Categories and cohomology theories, Topology, 13, 293-312 (1974) · Zbl 0284.55016 [9] Segal, G., Operations in stable homotopy theory, New Developments in Topology (1974), Cambridge University Press: Cambridge University Press Cambridge, London Mathematical Society Lecture Note Series II · Zbl 0274.55016 [10] Waldhausen, F., Algebraic \(K\)-theory of generalized free products, Ann. of Math., 108, 135-256 (1975) [11] Waldhausen, F., Operations in the algebraic \(K\)-theory of spaces, (Lecture Notes in Mathematics, 967 (1982), Springer: Springer Berlin), 390-409 [12] Waldhausen, F., Algebraic \(K\)-theory of spaces, (Lecture Notes in Mathematics, 1126 (1985), Springer: Springer Berlin), 318-419 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.