Date: Wed, 11 Feb 1998 12:19:08 -0800
From: David Espinosa <espinosa@kestrel.edu>
Subject: decompositions of topoi


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