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| 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. | ||
| J(S) | the sieve on an object X generated by a set S of maps to X. | ||
| Â(X) | the set of normal sieves on an object X. | ||
| FD(X) | (or simply F(X)) the set of D-sieves on an object X for a divisor D. | ||