Mackey systems of monoidal categories and G-spectra

Kazuhisa Shimakawa

doi:10.1007/BF00535647

Mackey systems of monoidal categories and G-spectra

Kazuhisa Shimakawa

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We construct an equivariant infinite loop space machine denned on certain class of monoidal O_G-categories which have built-in Mackey structure. Applications include the equivariant infinite delooping of the classifying space BF(G) for stable spherical G-fibrations and also the construction of an infinite loop G-space E(X, G) with π₀^HE(X, G) naturally isomorphic to the equivariant Whitehead groups Wh_H(X) of given G-space X.

Original language	English
Pages (from-to)	373-394
Number of pages	22
Journal	K-Theory
Volume	5
Issue number	4
DOIs	https://doi.org/10.1007/BF00535647
Publication status	Published - Jul 1 1991

Keywords

G-spectrum
Mackey system of monoidal categories
equivariant Whitehead group
spherical G-fibration

ASJC Scopus subject areas

Mathematics(all)

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10.1007/BF00535647

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AB - We construct an equivariant infinite loop space machine denned on certain class of monoidal OG-categories which have built-in Mackey structure. Applications include the equivariant infinite delooping of the classifying space BF(G) for stable spherical G-fibrations and also the construction of an infinite loop G-space E(X, G) with π0HE(X, G) naturally isomorphic to the equivariant Whitehead groups WhH(X) of given G-space X.

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KW - spherical G-fibration

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Mackey systems of monoidal categories and G-spectra

Abstract

Keywords

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