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arXiv · 2103.15785

Dualizable objects in stratified categories and the 1-dimensional bordism hypothesis for recollements

Grigory Kondyrev·Aaron Mazel-Gee·Jay Shah
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Abstract

Given a monoidal $\infty$-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 $\infty$-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 $\infty$-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.

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BibTeXRIS

Grigory Kondyrev, Aaron Mazel-Gee, Jay Shah. 2021-03-29. Dualizable objects in stratified categories and the 1-dimensional bordism hypothesis for recollements. https://arxiv.org/abs/2103.15785

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