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Aspects of topoi

Published online by Cambridge University Press:  17 April 2009

Peter Freyd
Peter Freyd
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadeiphia, Pennsylvania, USA.
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Abstract

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After a review of the work of Lawvere and Tierney, it is shown that every topos may be exactly embedded in a product of topoi each with 1 as a generator, and near-exactly embedded in a power of the category of sets. Several metatheorems are then derived. Natural numbers objects are shown to be characterized by exactness properties, which yield the fact that some topoi can not be exactly embedded in powers of the category of sets, indeed that the “arithmetic” arising from a topos dominates the exactness theory. Finally, several, necessarily non-elementary, conditions are shown to imply exact embedding in powers of the category of sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 1 , August 1972 , pp. 1 - 76
Copyright
Copyright © Australian Mathematical Society 1972

References

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