Suppose A is a category with a strict initial object 0 . Recall that an object P in A is called simple if any non-initial map to P is epic.
P is a simple spot.
X are two maps in A . A category is called simple if the class of simple objects is unidense . Since any reduced atomic object is simple , any reduced atomic category is simple. One can show that a category A is simple iff it has a simple functor E . Set is a Zariski topology.