  We prove that a pairing between the Fukaya category and the oo-category of
Lagrangian cobordisms respects mapping cones. This is another step toward
constructing a lift of Fukaya categories to the level of spectra (in the sense
of stable homotopy theory). As corollaries, we show that the map in our
previous work from cobordism groups to Floer cohomology lifts to the level of
spectra, and one also recovers some results of Biran and Cornea for what we
call "vertically collared" cobordisms.
