#
Glueing Analysis for Complemented Subtoposes

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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.

Keywords: Artin glueing, complemented subtoposes, complemented sublocale, locally
closed subtoposes, locally closed sublocale, prolongation by 0, extension by 0.

1991 MSC: 18B25.

*Theory and Applications of Categories*, Vol. 2, 1996, No. 9, pp 100-112.

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