Orbital presheaves in equivariant infinite loop space theory

Hana Jia Kong; J. Peter May; Foling Zou

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arXiv · 2607.12141

Orbital presheaves in equivariant infinite loop space theory

Hana Jia Kong·J. Peter May·Foling Zou

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Abstract

Let $G$ be a finite group. Using a new kind of operad, we axiomatize and explore an infinite loop space machine that constructs (genuine) $G$-spectra from suitably structured functors on orbital presheaves, which are just contravariant functors from the orbit category of $G$ to based spaces. The theory leads unexpectedly to a new operadic description of Mackey functors and hence to a definition of ``topological Mackey functors" and a construction of their associated $G$-spectra. It also leads to Picard $G$-spectra, Azumaya ring $G$-spectra, and Brauer $G$-spectra. These constructions raise many unanswered questions.

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BibTeX RIS

Hana Jia Kong, J. Peter May, Foling Zou. 2026-07-13. Orbital presheaves in equivariant infinite loop space theory. https://arxiv.org/abs/2607.12141

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