  For any small involutive quantaloid Q we define, in terms of symmetric
quantaloid-enriched categories, an involutive quantaloid Rel(Q) of Q-sheaves
and relations, and a category Sh(Q) of Q-sheaves and functions; the latter is
equivalent to the category of symmetric maps in the former. We prove that
Rel(Q) is the category of relations in a topos if and only if Q is a modular,
locally localic and weakly semi-simple quantaloid; in this case we call Q a
Grothendieck quantaloid. It follows that Sh(Q) is a Grothendieck topos whenever
Q is a Grothendieck quantaloid. Any locale L is a Grothendieck quantale, and
Sh(L) is the topos of sheaves on L. Any small quantaloid of closed cribles is a
Grothendieck quantaloid, and if Q is the quantaloid of closed cribles in a
Grothendieck site (C,J) then Sh(Q) is equivalent to the topos Sh(C,J). Any
inverse quantal frame is a Grothendieck quantale, and if O(G) is the inverse
quantal frame naturally associated with an \'etale groupoid G then Sh(O(G)) is
the classifying topos of G.
