#### Volume 9, issue 4 (2009)

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Permutative categories, multicategories and algebraic $K$–theory

### A D Elmendorf and M A Mandell

Algebraic & Geometric Topology 9 (2009) 2391–2441
##### Abstract

We show that the $K$–theory construction of our paper [Adv. Math 205 (2006) 163-228], which preserves multiplicative structure, extends to a symmetric monoidal closed bicomplete source category, with the multiplicative structure still preserved. The source category of [op cit], whose objects are permutative categories, maps fully and faithfully to the new source category, whose objects are (based) multicategories.

##### Keywords
$K$–theory, permutative category, multicategory
##### Mathematical Subject Classification 2000
Primary: 19D23, 55U99
Secondary: 55P42, 18D10, 18D50