  In this paper, we generalize the construction method of schemes to other
algebraic categories, and show that the category of coherent schemes can be
characterized by a universal property, if we fix the class of Grothendieck
topology. Also, we introduce the notion of $\scr{C}$-schemes, which is a
further generalization of coherent schemes and still shares common properties
with ordinary schemes.

Algebraic Geometry;Category Theory