  We study the category of matrix factorizations associated to the germ of an
isolated hypersurface singularity. This category is shown to admit a compact
generator which is given by the stabilization of the residue field. We deduce a
quasi-equivalence between the category of matrix factorizations and the dg
derived category of an explicitly computable dg algebra. Building on this
result, we employ a variant of Toen's derived Morita theory to identify
continuous functors between matrix factorization categories as integral
transforms. This enables us to calculate the Hochschild chain and cochain
complexes of these categories. Finally, we give interpretations of the results
of this work in terms of noncommutative geometry based on dg categories.
