AN UN-DELOOPED VERSION OF ALGEBRAIC K-THEORY
Autor(en): | GUNNARSSON, T SCHWANZL, R VOGT, RM WALDHAUSEN, F |
Stichwörter: | Mathematics; Mathematics, Applied; SPACES | Erscheinungsdatum: | 1992 | Herausgeber: | ELSEVIER SCIENCE BV | Journal: | JOURNAL OF PURE AND APPLIED ALGEBRA | Volumen: | 79 | Ausgabe: | 3 | Startseite: | 255 | Seitenende: | 270 | Zusammenfassung: | 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. |
ISSN: | 00224049 | DOI: | 10.1016/0022-4049(92)90053-I |
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geprüft am 19.05.2024