Operations in \(A\)-theory (Q1855453)
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scientific article; zbMATH DE number 1864810
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Operations in \(A\)-theory |
scientific article; zbMATH DE number 1864810 |
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Operations in \(A\)-theory (English)
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5 February 2003
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This paper gives a construction for Segal operations in the \(K\)-theory of categories with cofibrations, weak equivalences and a biexact pairing. The construction extends work of Grayson on exact categories. In particular the construction produces operations in the algebraic \(K\)-theory of spaces (\(A\)-theory); these are shown to be the operations used by Waldhausen in the proof of the \(A\)-theory Kahn-Priddy theorem. The total Segal operation is shown to be an infinite loop map.
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algebraic K-theory of spaces
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A-theory
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Segal operation
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Kahn-Priddy theorem
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infinite loop map
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