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Book Cover
E-book
Author Moerdijk, Ieke

Title Proper maps of toposes / I. Moerdijk, J.J.C. Vermeulen
Published Providence, R.I. : American Mathematical Society, ©2000

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Description 1 online resource (ix, 108 pages) : illustrations
Series Memoirs of the American Mathematical Society, 1947-6221 ; v. 705
Memoirs of the American Mathematical Society ; no. 705. 0065-9266
Contents Introduction I. Proper maps II. Separated maps III. Tidy maps IV. Strongly separated maps V. Relatively tidy maps and lax descent
Summary We develop the theory of compactness of maps between toposes, together with associated notions of separatedness. This theory is built around two versions of "propriety" for topos maps, introduced here in a parallel fashion. The first, giving what we simply call "proper" maps, is a relatively weak condition due to Johnstone. The second kind of proper maps, here called "tidy", satisfy a stronger condition due to Tierney and Lindgren. Various forms of the Beck-Chevalley condition for (lax) fibered product squares of toposes play a central role in the development of the theory. Applications include a version of the Reeb stability theorem for toposes, a characterization of hyperconnected Hausdorff toposes as classifying toposes of compact groups, and of strongly Hausdorff coherent toposes as classifiying toposes of profinite groupoids. Our results also enable us to develop further particular aspects of the factorization theory of geometric morphisms studied by Johnstone. Our final application is a (so-called lax) descent theorem for tidy maps between toposes. This theorem implies the lax descent theorem for coherent toposes, conjectured by Makkai and proved earlier by Zawadowski
Bibliography Includes bibliographical references (pages 107-108)
Notes English
Print version record
Subject Toposes.
Mappings (Mathematics)
Mappings (Mathematics)
Toposes
Form Electronic book
Author Vermeulen, J. J. C. (Jacob Johan Caspar), 1957-
ISBN 9781470402969
1470402963