Abstract
Motivated by calculations of motivic homotopy groups, we give widely attained conditions under which operadic algebras and modules thereof are preserved under (co)localization functors.
Highlights
Operads are key mathematical devices for organizing hierarchies of higher homotopies in a variety of settings
This paper is a sequel to our work on operads in the context of the slice filtration in motivic homotopy theory [10]
The problem we address here is that of preservation of algebras over colored operads, and modules over such algebras, under Bousfieldlocalization functors
Summary
Operads are key mathematical devices for organizing hierarchies of higher homotopies in a variety of settings. This paper is a sequel to our work on operads in the context of the slice filtration in motivic homotopy theory [10]. The problem we address here is that of preservation of algebras over colored operads, and modules over such algebras, under Bousfield (co)localization functors. Our main motivation for studying the mentioned problem of preservation of algebras is rooted in Morel’s p1-conjecture [16, 17]. The solution of Morel’s p1-conjecture [17] involves an explicit calculation in the slice spectral sequence of the motivic sphere spectrum. Our main results on preservation of algebras and modules under Bousfield (co)localization functors are shown in §3 and §4. We review tensor-closed sets of objects in a homotopy category, the Reedy model structure, operadic algebras, and modules over such algebras
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