2021/03/29 by Kondyrev, Grigory, Mazel-Gee, Aaron, Shah, Jay
#18N70 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2103.15785
Given a monoidal ∞-category C equipped with a monoidal recollement, we give a simple criterion for an object in C to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them. Predicated on this, we then characterize dualizability in any monoidally stratified ∞-category in terms of stratumwise dualizability and a projection formula for the links. Using our criterion, we prove a 1-dimensional bordism hypothesis for symmetric monoidal recollements. Namely, we provide an algebraic enhancement of the 1-dimensional framed bordism ∞-category that corepresents dualizable objects in symmetric monoidal recollements. We also give a number of examples and applications of our criterion drawn from algebra and homotopy theory, including equivariant and cyclotomic spectra and a multiplicative form of the Thom isomorphism.