Multifunctorial Equivariant Algebraic K-Theory

By Donald Yau

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.

• Format: Paperback
• Language: English
• ISBN: 1009775200
• ISBN13: 9781009775205
• Release Date: June 2026
• Publisher: Cambridge University Press
• Length: 484 Pages
• Weight: 1.42 lbs.
• Dimensions: 1.0" x 6.0" x 9.0"