Operads in Unstable Global Homotopy Theory

Abstract

We study operads in unstable global homotopy theory, which is the homotopy theory of spaces with compatible actions by all compact Lie groups. We show that the theory of these operads works remarkably well, as for example it is possible to give a model structure for the category of algebras over any such operad. We define global $E_{\infty }$-operads, a good generalization of $E_{\infty }$-operads to the global setting, and we give a rectification result for algebras over them.

arXiv comment33 pages, final published version, minor changes, updated bibliography

References in corpus (12)

• Algebras and modules in monoidal model categories
• Rings, modules, and algebras in infinite loop space theory
• Global homotopy theory
• Diagram spaces and symmetric spectra
• Operads, Algebras and Modules in General Model Categories
• Homotopy theory for algebras over polynomial monads
• Admissibility and rectification of colored symmetric operads
• Homotopy theory of modules over operads in symmetric spectra
• Equivariant iterated loop space theory and permutative G-categories
• Homotopy theory of symmetric powers
• A model structure via orbit spaces for equivariant homotopy
• Global $N_{\infty }$-operads

Cited by in corpus (2)

• Genuine vs. naïve symmetric monoidal G-categories
• Parametrized stability and the universal property of global spectra