When "Ellis D. Cooper" <xtalv1@netropolis.net> asks,
What are the general rules for calculating the sub-object classifier of a topos? Or, for what class of toposes is there an algorithm for calculating the sub-object classifier of its members?
I imagine the sort of response he hoped for is one like: In a presheaf topos, the suboject classifier Ω can be unraveled, from its universal property, by help of the Yoneda Lemma, as each of the various values Ω(X) that Ω must take at an object X "is" the set of natural transformations from hom(-, X) to Ω, which, in turn, "is" the set of subfunctors of the representable functor hom(-, X). I'll let others formulate similarly "algorhythmic" proposals for other sorts of topoi (comonadic ones, sheaves, etc.). Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]