  We consider a definition of the Fukaya category of a singular hypersurface
proposed by Auroux, given by localizing the Fukaya category of a nearby fiber
at Seidel's natural transformation, and show that this possesses several
desirable properties. Firstly, we prove an A-side analog of Orlov's derived
Kn\"orrer periodicity theorem by showing that Auroux' category is derived
equivalent to the Fukaya-Seidel category of a higher-dimensional
Landau-Ginzburg model. Secondly, we describe how this definition should imply
homological mirror symmetry at various large complex structure limits, in the
context of forthcoming work of Abouzaid-Auroux and Abouzaid-Gross-Siebert.
