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A topos is a category that behaves very much like the category of sets and possesses a good notion of localization. Related to topos are: sheaves, presheaves, descent, stacks, localization,...
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`Topos' with alternate subobject lattice?
We know that for any topos E, and for any object A in E, the subobjects of A, Sub(A), form a Heyting lattice.
Does anybody know of any sort of modification of the definition of a topos that makes Sub …