A higher Mackey functor description of algebras over an N_∞-operad

2024/02/19 by Marc, Gregoire
#55P91 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.12447

Abstract

Suppose G is a finite group. In this paper, we construct an equivalence between the ∞-category of algebras over an N_∞-operad O associated to a G-indexing system I and the corresponding ∞-category of higher incomplete I-Mackey functors with value in spaces. We use the universal property of the incomplete (2, 1)-category of spans of finite G-sets \mathscrA_I to construct a functor from \mathscrA_I to the 2-category of I-normed symmetric monoidal categories of Rubin. We then show that the left Kan extension of the composition of this functor with the core functor is an equivalence.

Related

• Parametrized (higher) semiadditivity and the universality of spans
• Mackey functors from the viewpoint of double category theories
• Goodwillie calculus and Mackey functors
• On higher monoidal ∞-categories
• ∞-operads as symmetric monoidal ∞-categories