




0 
an initial object in an analytic category. 


1 
a terminal object in an analytic category. 


D(G) 
the class of open effective monos for a framed topology G. 


Loc(X) 
the dual of the poset of reduced strong subobjects of
an object X in an analytic geometry. 


R(X) 
the set of strong subobjects of an object X in an analytic category. 


rad(X) 
the radical of an object X in an analytic category,
which is the unipotent reduced strong subobject of X. 


red(X) 
the reduced model
of an object X in an analytic category, which is the largest
reduced strong subobject of X. 


Spec(X) 
the set of prime subobjects of an object X in an analytic category. 


S(X) 
the set of reduced strong subobjects of an object X in an analytic
category. 


ØS 
the set of maps to an object X which is disjoint with a set
S of maps to X. 


T(G) 
The collection of open effective covers for a framed topology G. 


sie(S) 
the sieve on an object X generated by a set S
of maps to X. 


(X) 
the set of normal sieves on an object X. 


F_{D}(X) 
(or simply F(X)) the set of Dsieves
on an object X for a divisor D. 








