 For any morphism "f" in formula_2 there is an associated "pullback functor" formula_8 which is key in the proof of the theorem.For any other morphism "g" in formula_2 which shares the same codomain as "f", their product formula_10 is the diagonal of their pullback square, and the morphism which goes from the domain of formula_10 to the domain of "f" is opposite to "g" in the pullback square, so it is the pullback of "g" along "f", which can be denoted as formula_12.Note that a topos formula_2 is isomorphic to the slice over its own terminal object, i.e.