An Inverse $K$-Theory Functor

Thomason showed that the $K$-theory of symmetric monoidal categories models all connective spectra. This paper describes a new construction of a permutative category from a $\Gamma$-space, which is then used to re-prove Thomason's theorem and a non-completed variant.

2010 Mathematics Subject Classification: Primary 19D23, 55P47; Secondary 18D10, 55P42

Keywords and Phrases: Gamma space, permutative category, connective spectrum

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