  We construct a category, $\Omega$, of which the objects are pointed
categories and the arrows are pointed correspondences. The notion of a "spec
datum" is introduced, as a certain relation between categories, of which one
has been given a Grothendieck topology. A "geometry" is interpreted as a
sub-category of $\Omega$, and a formalism is given by which such a subcategory
is to be associated to a spec datum, reflecting the standard construction of
the category of schemes from the category of rings by affine charts.
