Symmetric monoidal g-categories and their strictification

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

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8 Scopus citations

Abstract

We give an operadic definition of a genuine symmetric monoidal G-category, and we prove that its classifying space is a genuine E- infty G-space. We do this by developing some very general categorical coherence theory. We combine results of Corner and Gurski, Power and Lack to develop a strictification theory for pseudoalgebras over operads and monads. It specializes to strictify genuine symmetric monoidal G-categories to genuine permutative G-categories. All of our work takes place in a general internal categorical framework that has many quite different specializations. When G is a finite group, the theory here combines with previous work to generalize equivariant infinite loop space theory from strict space level input to considerably more general category level input. It takes genuine symmetric monoidal G-categories as input to an equivariant infinite loop space machine that gives genuine Omega -G-spectra as output.

Original languageEnglish
Pages (from-to)207-246
Number of pages40
JournalQuarterly Journal of Mathematics
Volume71
Issue number1
DOIs
StatePublished - Mar 13 2020

Bibliographical note

Publisher Copyright:
© 2019 The Author(s) 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals. permissions@oup.com.

ASJC Scopus subject areas

  • General Mathematics

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