  We show that there is a bijection between the subtoposes of the classifying
topos of a geometric theory T over a signature L and the closed geometric
theories over L which are `quotients' of the theory T; next, we analyze how
classical topos-theoretic constructions on the lattice of subtoposes of a given
topos can be transferred, via the bijection above, to logical constructions in
the corresponding lattice of theories.
