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- W3140386380 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." @default.
- W3140386380 created "2021-04-13" @default.
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- W3140386380 date "2021-03-29" @default.
- W3140386380 modified "2023-09-27" @default.
- W3140386380 title "Dualizable objects in stratified categories and the 1-dimensional bordism hypothesis for recollements" @default.
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