  We present a solution to the problem of defining a counterpart in Algebraic
Set Theory of the construction of internal sheaves in Topos Theory. Our
approach is general in that we consider sheaves as determined by
Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume
only a weakening of the axioms for small maps originally introduced by Joyal
and Moerdijk, thus subsuming the existing topos-theoretic results.
