Basic constructions in the 𝐾-theory of homotopy ring spaces

Schwänzl, R.; Vogt, R. M.

doi:10.1090/S0002-9947-1994-1116318-5

Basic constructions in the $K$-theory of homotopy ring spaces
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Trans. Amer. Math. Soc. 341 (1994), 549-584 Request permission

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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