Algebraic & Geometric Topology

Permutative categories, multicategories and algebraic $K$–theory

A D Elmendorf and M A Mandell

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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.

Article information

Source
Algebr. Geom. Topol., Volume 9, Number 4 (2009), 2391-2441.

Dates
Received: 9 March 2009
Revised: 1 September 2009
Accepted: 7 October 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513797088

Digital Object Identifier
doi:10.2140/agt.2009.9.2391

Mathematical Reviews number (MathSciNet)
MR2558315

Zentralblatt MATH identifier
1205.19003

Subjects
Primary: 19D23: Symmetric monoidal categories [See also 18D10] 55U99: None of the above, but in this section
Secondary: 55P42: Stable homotopy theory, spectra 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 18D50: Operads [See also 55P48]

Keywords
$K$–theory permutative category multicategory

Citation

Elmendorf, A D; Mandell, M A. Permutative categories, multicategories and algebraic $K$–theory. Algebr. Geom. Topol. 9 (2009), no. 4, 2391--2441. doi:10.2140/agt.2009.9.2391. https://projecteuclid.org/euclid.agt/1513797088


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