Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference6 articles.
1. Several new concepts: Lucid and concordant functors, pre-limits, pre-completeness, the continuous and concordant completions of categories
2. The meeting of the Midwest Category Seminar in Zurich August 24–30, 1970
3. [1] Cole J.C. , “Categories of sets and models of set theory”, Aarhus Universitet, Matematisk Institut, Preprint series, 52, 1971.
Cited by
187 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献