Biased permutative equivariant categories

For a finite group G, we introduce the complete suboperad $Q_G$ of the categorical G-Barratt-Eccles operad $P_G$. We prove that $P_G$ is not finitely generated, but $Q_G$ is finitely generated and is a genuine $E_\infty$ G-operad (i.e., it is $N_\infty$ and includes all norms). For G cyclic of order...

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Hauptverfasser:	Bangs, Kayleigh, Binegar, Skye, Kim, Young, Ormsby, Kyle, Osorno, Angélica M, Tamas-Parris, David, Xu, Livia
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Algebraic Topology Mathematics - Category Theory
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Zusammenfassung:	For a finite group G, we introduce the complete suboperad $Q_G$ of the categorical G-Barratt-Eccles operad $P_G$. We prove that $P_G$ is not finitely generated, but $Q_G$ is finitely generated and is a genuine $E_\infty$ G-operad (i.e., it is $N_\infty$ and includes all norms). For G cyclic of order 2 or 3, we determine presentations of the object operad of $Q_G$ and conclude with a discussion of algebras over $Q_G$, which we call biased permutative equivariant categories.
DOI:	10.48550/arxiv.1907.00933