Permutative categories, multicategories and algebraic K–theory

Elmendorf, A D; Mandell, M A

doi:10.2140/agt.2009.9.2391

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ISSN (electronic): 1472-2739

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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

DOI: 10.2140/agt.2009.9.2391

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

References

Publication

Received: 9 March 2009

Revised: 1 September 2009

Accepted: 7 October 2009

Published: 3 November 2009

Authors

A D Elmendorf
Department of Mathematics Purdue University Calumet Hammond, IN 46323

M A Mandell
Department of Mathematics Indiana University Bloomington, IN 47405

Volume 9, issue 4 (2009)