## An inverse $K$-theory functor

### Summary

Summary: 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.

### Mathematics Subject Classification

19D23, 55P47, 18D10, 55P42

### Keywords/Phrases

gamma space, permutative category, connective spectrum