geometrically this is the fiber of formula_12 over formula_13 and abstractly it is the Yoneda functor represented by formula_2 in the category of schemes over formula_1. The functor formula_16 is typically not representable in formula_4; however, it is pro-representable in formula_4, in fact by Galois covers of formula_1. This means that we have a projective system formula_20 in formula_4, indexed by a directed set formula_22 where the formula_23 are Galois covers of formula_1, i.e., finite étale schemes over formula_1 such that formula_26. It also means that we have given an isomorphism of functors