Let a category A be locally finitely presentable, and let B be a full reflective subcategory for which the inclusion B ---> A is FINITARY - that is, preserves filtered colimits. Is there necessarily in A a set of arrows of the form k:M ---> N, where M and N are finitely presentable, such that B consists of the objects ORTHOGONAL to each k, in the sense that an object a of A is in B if & only if each A(k,a):A(N,a) ---> A(M,a) is invertible? It is easy to see that it suffices to answer the question when A is a presheaf category P; just express A as a finitarily reflective subcategory of such a P. It is of course true that B is locally finitely presentable, & is therefore expressible as the full subcategory of some presheaf category Q, given by the objects of Q orthogonal to a set of arrows between locally-presentables; that is not the point. Max Kelly, 17 May.