Combinatorial $N_{\infty }$ operads

Abstract

We prove that the homotopy theory of $N_{\infty }$ operads is equivalent to a homotopy theory of discrete operads, and we construct free and associative operadic realizations of every indexing system. This resolves a conjecture of Blumberg and Hill in the affirmative.

37 pages, restructured discussion

References in corpus (7)

• Encoding Equivariant Commutativity via Operads
• Genuine equivariant operads
• Incomplete Tambara functors
• Equivariant stable categories for incomplete systems of transfers
• Characterizations of equivariant Steiner and linear isometries operads
• Categorifying the algebra of indexing systems
• Normed symmetric monoidal categories

Cited by in corpus (7)

• Encoding Equivariant Commutativity via Operads
• Genuine equivariant operads
• Multiplicativity of the idempotent splittings of the Burnside ring and the G-sphere spectrum
• Global $N_{\infty }$-operads
• Lifting $N_{\infty }$ operads from conjugacy data
• Global transfer systems of abelian compact Lie groups
• Realization of saturated transfer systems on cyclic groups of order $p^n{q}^m$ by linear isometries $N_{\infty }$-operads