  We provide a precise description, albeit in the situation of standard
categories, of the quantization functor Sum proposed by D.S. Freed, M.J.
Hopkins, J. Lurie, and C. Teleman in a way enough abstract and flexible to
suggest that an extension of the construction to the general context of higher
categories should indeed be possible. Our method is in fact based primarily on
dualizability and adjunction data, and is well suited for the homotopical
setting. The construction also sheds light on the need of certain rescaling
automorphisms, and in particular on the nature and properties of the Nakayama
isomorphism.
