* decompositions of topoi
@ 1998-02-11 20:19 David Espinosa
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From: David Espinosa @ 1998-02-11 20:19 UTC (permalink / raw)
To: categories; +Cc: espinosa
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
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