 Now apply formula_23 to formula_21.This yields
so this is how the pullback functor formula_23 maps objects of formula_19 to formula_28.Furthermore, note that any element "C" of the base topos is isomorphic to formula_29, therefore if formula_30 then formula_31 and formula_32 so that formula_23 is indeed a functor from the base topos formula_2 to its slice formula_28.