Glueing Analysis for Complemented Subtoposes
Anders Kock and Till Plewe
We prove how any (elementary) topos may be reconstructed from
the data of two complemented subtoposes together with a pair
of left exact ``glueing functors''. This generalizes the
classical glueing theorem for toposes, which deals with the
special case of an open subtopos and its closed complement.
Our glueing analysis applies in a particularly simple form to
a locally closed subtopos and its complement, and one of the
important properties (prolongation by zero for abelian groups)
can be succinctly described in terms of it.