Categorical Geometry Chapter 3 Section 3.6 Zhaohua Luo 3.6. Let A be an analytic geometry. If P is a prime of X , which is contained in the join W of two strong subobjects U and V of X , then P is contained in U or V .
P is the join of U P and V P .
The other direction is obvious. Y is a map. The join of all the primes of X is the radical of X . We prove that W is unipotent. We have to show that t is not disjoint with W .