Page 216 of Lambek and Scott describes how to decompose a topos via a cocover, that is, a monomorphism in Top M : T -> prod(i in I) T/P_i where P_i are the prime filters of T. (1) Does anyone know where to find a more extended discussion of this decomposition? (2) Is there a dual decomposition via a cover, that is, an epimorphism E : sum(i in I) T_i -> T ? This construction could already be in Lambek and Scott, but I haven't had the chance to study L&S in detail, so I'm still in over my head. The conjecture (due to Y.V. Srinivas) is that these ideas are useful for structuring a database of theories by breaking theories into their smallest reasonable subtheories. See the paper on Specware by Srinivas and Jullig on Kestrel's website http://www.kestrel.edu for more information. So far, this work has dealt with covers of theories, rather than cocovers, whence my question. David Espinosa Kestrel Institute