  We present a simple way of incorporating the structure of contextual
extensions into quantum gravity models. The contextual extensions of
$C^*$-algebras, originally proposed for contextual hidden variables, are
generalized to the cones indexed by the contexts and their limit in a category.
By abstracting the quantum gravity models as functors, we study the contextual
extensions as the categorical limits of these functors in several quantum
gravity models. Such contextual extensions of quantum gravity models are useful
for building topos-theoretic models of quantum gravity.
