Multifunctorial equivariant algebraic K-theory Donald Yau

Format:

Book

Author/Creator:

Yau, Donald Y. (Donald Ying), 1977- author.

Series:

London Mathematical Society lecture note series ; 503.

London Mathematical Society lecture note series 503

Language:

English

Subjects (All):

K-theory.

Physical Description:

1 online resource

Place of Publication:

Cambridge Cambridge University Press 2026

Summary:

"A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. This book answers this question positively by constructing an enriched multifunctor from the G-categorically enriched multicategory of O-pseudoalgebras to the symmetric monoidal category of orthogonal G-spectra, for a compact Lie group G and a 1-connected pseudo-commutative G-categorical operad O. As the main application of its enriched multifunctoriality, this machine preserves all equivariant algebraic structures parametrized by multicategories enriched in either G-spaces or G-categories. In addition to highly detailed proofs of all the main results, this work also reviews relevant concepts, including orthogonal G-spectra. Appendices provide the necessary background on symmetric monoidal categories, multicategories, and classifying space. Clearly written and well organized, this book will be a useful reference for researchers and graduate students for years to come"-- Cambridge Core

Contents:

Pseudo-commutative operads and operadic pseudoalgebras

GCat-multicategories of operadic pseudoalgebras

Symmetric monoidal closed category of G-G-categories

GCat-multifunctors from operadic pseudoalgebras to G-G-categories

Equivariant orthogonal spectra

From G-G-categories to G-G-spaces

Symmetric GTop-monoidal equivariant K-theory

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (Cambridge Core, viewed June 5, 2026)

Other Format:

Print version Yau, Donald Y. (Donald Ying), 1977- Multifunctorial equivariant algebraic K-theory

ISBN:

9781009775175

1009775170

9781009775199

1009775197

OCLC:

1571483331

Access Restriction:

Restricted for use by site license