Thus a locally disjunctable coherent analytic category is a spatial analytic geometry , which is simply called a coherent analytic geometry . In the following we assume A is a coherent analytic geometry. Thus any affine open subset is also quasi-compact. Since any unipotent strong subobject of X induces a unipotent strong subobject of P , we only need to prove that P is disjoint with any non-unipotent strong subobject V of X . If X is primary then any non-initial analytic mono is epic.
X is epic coflat.
X with T primary. T be the fractional hull of T . Since p T is generic, so is the composite tp T . Thus tp T . Thus m is the smallest strong mono such that tp T can be factored through.