Summary: Sheaf Representation for Topoi
S. Awodey \Lambda
Autumn 1997
Abstract
It is shown that every (small) topos is equivalent to the category of
global sections of a sheaf of so­called hyperlocal topoi, improving on
a result of Lambek & Moerdijk. It follows that every boolean topos
is equivalent to the global sections of a sheaf of well­pointed topoi.
Completeness theorems for higher­order logic result as corollaries.
The main result of this paper is the following.
Theorem (Sheaf representation for topoi). For any small topos E,
there is a sheaf of categories e
E on a topological space, such that:
(i) E is equivalent to the category of global sections of e
E,
(ii) every stalk of e
E is a hyperlocal topos.
Moreover, E is boolean just if every stalk of e
E is well­pointed.
Before defining the term ``hyperlocal,'' we indicate some of the back­

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

Collections: Mathematics