Product-preserving sub-representables

Dear categorists, I've recently had reason to consider presheaves P : C^op --> Set on a category C with the following two properties: - P preserves all small products (i.e. sends coproducts in C to products in Set), and - P is a subfunctor of a representable presheaf. Is anyone aware of situations where presheaves with both of these properties are significant? In particular, I'm interested in categories C for which every such P is representable. The only examples I'm aware of are Set, Vect, and any poset with arbitrary joins. Does anyone know of any more? Best wishes, Tom Avery -- [For admin and other information see: http://www.mta.ca/~cat-dist/ ]