  The homotopy theory of small functors is a useful tool for studying various
questions in homotopy theory. In this paper, we develop the homotopy theory of
small functors from spectra to spectra, and study its interplay with
Spanier-Whitehead duality and enriched representability in the dual category of
spectra.
  We note that the Spanier-Whitehead duality functor $D\colon
\mathrm{Sp}\rightarrow \mathrm{Sp}^{\mathrm{op}}$ factors through the category
of small functors from spectra to spectra and construct a new model structure
on the category of small functors, which is Quillen equivalent to
$\mathrm{Sp}^{\mathrm{op}}$. In this new framework for the Spanier-Whitehead
duality, $\mathrm{Sp}$ and $\mathrm{Sp}^{\mathrm{op}}$ are full subcategories
of the category of small functors and dualization becomes just a fibrant
replacement in our new model structure.
