Products and Duality in Categories with Cofibrations and Weak Equivalences
نویسندگان
چکیده
The natural transformation Ξ from L–theory to the Tate cohomology of Z/2 acting on K–theory (constructed in [WW2] and [WW3]) commutes with external products. Corollary: The Tate cohomology of Z/2 acting on the K–theory of any ring with involution is a generalized Eilenberg–MacLane spectrum, and it is 4–periodic.
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Duality in Waldhausen Categories
We develop a theory of Spanier–Whitehead duality in categories with cofibrations and weak equivalences (Waldhausen categories, for short). This includes L–theory, the involution on K–theory introduced by [Vo] in a special case, and a map Ξ relating L–theory to the Tate spectrum of Z/2 acting on K–theory. The map Ξ is a distillation of the long exact Rothenberg sequences [Sha], [Ra1], [Ra2], inc...
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