  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.
