  For a collection of subcategories satisfying a fixed set of conditions, for
example thick subcategories of a triangulated category, we define a topological
space called classifying space of subcategories. We show that this space
classifies various prime subcategories in the sense that they bijectively
correspond to the closed subsets of the classifying space. Many well-known
results of subcategory classification fit into this framework. An example which
cannot be classified by a topological space in the above sense is also given.
