Multiplicative equivariant \(K\)-theory and the Barratt-Priddy-Quillen theorem

DOI10.1016/j.aim.2023.108865OpenAlexW3135326418WikidataQ122709910 ScholiaQ122709910MaRDI QIDQ2685684

Mona Merling, Angélica M. Osorno, J. Peter May, Bertrand J. Guillou

Publication date: 22 February 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.13246

zbMATH Keywords

\(K\)-theoryoperadsmulticategoriesmultifunctorsmultiplicative equivariant infinite loop spaces

Mathematics Subject Classification ID

Equivariant homotopy theory in algebraic topology (55P91) Equivariant (K)-theory (19L47) Symmetric monoidal categories (19D23) Loop space machines and operads in algebraic topology (55P48) Enriched categories (over closed or monoidal categories) (18D20) Topological categories, foundations of homotopy theory (55U40) Internal categories and groupoids (18D40) Non-symmetric operads, multicategories, generalized multicategories (18M65)

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Cites Work

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• Units of equivariant ring spectra
• The spectra associated to permutative categories
• Multiplicative infinite loop space theory
• Enriched categories as a free cocompletion
• Universality of multiplicative infinite loop space machines
• Permutative categories, multicategories and algebraic \(K\)-theory
• Equivariant stable homotopy theory. With contributions by J. E. McClure
• A general coherence result
• Infinite loop G-spaces associated to monoidal G-graded categories
• Pairings of categories and spectra
• \(E_\infty\) ring spaces and \(E_\infty\) ring spectra. With contributions by Frank Quinn, Nigel Ray, and Jorgen Tornehave
• The uniqueness of infinite loop space machines
• A symmetric monoidal and equivariant Segal infinite loop space machine
• Categories and cohomology theories
• Homotopy invariant algebraic structures on topological spaces
• Pseudo-commutative monads and pseudo-closed 2-categories
• Codescent objects and coherence
• Spectral Mackey functors and equivariant algebraic \(K\)-theory. II.
• A union theorem for cofibrations
• Equivariant iterated loop space theory and permutative \(G\)-categories
• Infinite loop spaces, and coherence for symmetric monoidal bicategories
• Rings, modules, and algebras in infinite loop space theory
• An adjunction theorem for locally equiconnected spaces
• The geometry of iterated loop spaces
• Internal categories, anafunctors and localisations
• Categorical Homotopy Theory
• What precisely are $E_{\infty}$ ring spaces and $E_{\infty}$ ring spectra?
• The construction of $E_{\infty}$ ring spaces from bipermutative categories
• On Spaces Having the Homotopy Type of a CW-Complex
• Fixed Set Systems of Equivariant Infinite Loop Spaces
• Cosmoi of Internal Categories
• HYPER-Γ-SPACES AND HYPERSPECTRA
• Γ-SPACES, ORIENTATIONS AND COHOMOLOGY OPERATIONS
• When is the Natural Map X →ΩΣX a Cofibration?
• SYMMETRIC MONOIDALG-CATEGORIES AND THEIR STRICTIFICATION
• Iterated icons