  We present a new strictification method for type-theoretic structures that
are only weakly stable under substitution. Given weakly stable structures over
some model of type theory, we construct equivalent strictly stable structures
by evaluating the weakly stable structures at generic contexts. These generic
contexts are specified using the categorical notion of familial
representability. This generalizes the local universes method of Lumsdaine and
Warren.
  We show that generic contexts can also be constructed in any category with
families which is freely generated by collections of types and terms, without
any definitional equality. This relies on the fact that they support
first-order unification. These free models can only be equipped with weak
type-theoretic structures, whose computation rules are given by typal
equalities. Our main result is that any model of type theory with weakly stable
weak type-theoretic structures admits an equivalent model with strictly stable
weak type-theoretic structures.
