If $E$ is a topos, is there a nice way to characterize the category of logical morphisms $E\to Set$? Is it complete and/or cocomplete?
The topos $Set$ geometrically represents a point; what does it logically represent?
If $E$ is a topos, is there a nice way to characterize the category of logical morphisms $E\to Set$? Is it complete and/or cocomplete? The topos $Set$ geometrically represents a point; what does it logically represent? 

