  We introduce systematic methods to construct Grothendieck categories from
colored quivers and develop a theory of the specialization orders on the atom
spectra of Grothendieck categories. We show that any partially ordered set is
realized as the atom spectrum of some Grothendieck category, which is an analog
of Hochster's result in commutative ring theory. We also show that there exists
a Grothendieck category which has empty atom spectrum but has nonempty
injective spectrum.
