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Basic constructions in the $ K$-theory of homotopy ring spaces


Authors: R. Schwänzl and R. M. Vogt
Journal: Trans. Amer. Math. Soc. 341 (1994), 549-584
MSC: Primary 55P47
DOI: https://doi.org/10.1090/S0002-9947-1994-1116318-5
MathSciNet review: 1116318
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Abstract: Using the language of category theory and universal algebra we formalize the passage from the permutative category of finitely generated free $ R$-modules to the algebraic $ K$-theory $ KR$ of $ R$ and thus make it applicable to homotopy ring spaces. As applications we construct a Waldhausen type of algebraic $ K$-theory for arbitrary homotopy ring spaces, show its equivalence with constructions of May and Steiner, prove its Morita invariance and show that the algebraic $ K$-theory $ KX$ of an $ {E_\infty }$ ring $ X$ is itself an $ {E_\infty }$ ring. Finally we investigate the monomial map $ Q(BX_ + ^\ast) \to KX$.


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DOI: https://doi.org/10.1090/S0002-9947-1994-1116318-5
Article copyright: © Copyright 1994 American Mathematical Society

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