Grothendieck topologies in computer science You may be interested in my paper "Geometric theories and databases", which I shall be presenting at the LMS Symposium on Applications of Categories in Computer Science this July in Durham. (I can send you a draft if you wish.) Its abstract is - <<< Domain theoretic understanding of databases as elements of powerdomains is modified to allow multisets of records instead of sets. This is related to geometric theories and classifying toposes, and it is shown that algebraic base domains lead to algebraic categories of models in two cases analogous to the lower (Hoare) powerdomain and Gunter's mixed powerdomain. >>> The results amount to saying that certain Grothendieck toposes are equivalent. But the flavour of the paper is not to describe these toposes concretely as categories of sheaves over sites, but to specify them less directly as classifying toposes of geometric theories. I believe it is important to understand that this can be done, for the geometric theories provide a much defter way of talking about Grothendieck toposes. Hence I would hope that although the paper does not mention sheaves or Grothendieck topologies, you would find it very useful. Note that "algebraic categories of models" refers to theories whose classifying toposes are actually presheaf categories, with no Grothendieck topologies required. But the theories proved equivalent to these are not prima facie algebraic, and so the work yields completeness results for them. Finally, let me mention that an underlying theme of the work is that geometric logic is the logic of finite observations (as discussed in my book "Topology via Logic" in the propositional case), and that the methods developed go far deeper than the database applications. Steve Vickers. (And can you send me a copy of the dissertation, please?)