Overview

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.

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9781009775205

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Donald Yau is a mathematician who specializes in algebraic topology and algebraic K-theory. He has published over fifty research articles and 15 books, including Homotopy Theory of Enriched Mackey Functors (Cambridge, 2025).

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