Combinatorial N∞ operads

Parametrized and equivariant higher algebra

“…Then one sees that I is a G-indexing system and these assignments are mutually inversenote that condition (5) holds since given U, U ′ G/H, the coproduct in F H is given by the composition U U ′ G/H G/H G/H. Consequently, by the work of Bonventre-Pereira [BP21], Gutiérrez-White [GW18], and Rubin [Rub21], we see that the commutative G-∞-operads are in bijection with the N ∞ -operads of Blumberg-Hill.…”

Equivariant homotopy commutativity for $G=C_{pqr}$

“…Blumberg and Hill showed that every operad determines an "indexing system" [BH15]. Rubin [Rub17], Gutierrez-White [GW18] and Bonventre-Pereira [BP17] independently showed that for every such indexing system one can construct a corresponding operad. Barnes-Balchin-Roitzheim [BBR19] showed that indexing systems are equivalent to the transfer systems given in the above version of this theorem.…”

SYMMETRIC MONOIDALG-CATEGORIES AND THEIR STRICTIFICATION

“…We discuss the philosophy behind Definition 0.3 in §3, where we also indicate relevant categorical questions that have been addressed by Rubin [29,30] in work complementary to ours. He works concretely in the equivariant context of N ∞ Goperads pioneered by Blumberg and Hill [6] and developed further by Rubin and others [7,14,29], and he compares our symmetric monoidal G-categories with the analogous but definitionally disparate context of G-symmetric monoidal categories of Hill and Hopkins [15]. We shall say a bit more about his work in §3.…”