Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/6203
Title: | Abelian Groups in a Topos of Sheaves on a Locale |
Authors: | Bhutani, Ravender Kiran |
Advisor: | Banaschewski, Bernhard |
Department: | Mathematics |
Keywords: | Mathematics;Mathematics |
Publication Date: | 1983 |
Abstract: | <p>This thesis is devoted to the study of Abelian Groups in the topos Shℒ of sheaves on a locale ℒ. The main topics considered are: injectivity, essential extensions of torsion groups, divisibility, purity, internal hom-functor, tensor product and flatness.</p> <p>We derive some general results about these notions. Also, we prove the Baer Criterion for injectivity in AbShℒ. For a well-ordered locale ℒ, we describe the injective hulls in AbShℒ and for some special locales we characterize the injectives in AbShℒ.</p> <p>We further discuss essential extensions of torsion groups and show amongst other things, that a first countable Hausdorff space X is discrete iff essential extensions in AbShX preserve torsion.</p> <p>Divisible groups are characterized here as absolutely pure groups. We discuss the internal adjointness between the tensor product and the internal hom-functor.</p> <p>Finally, we consider the notion of flatness, and show that the flat groups in AbShℒ are characterized the same way as in Ab, that is, flat = torsion free, and that A is flat in AbShℒ iff A* = [A,P] is an injective group, where P is an injective cogenerator.</p> |
URI: | http://hdl.handle.net/11375/6203 |
Identifier: | opendissertations/1531 2162 1262107 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Size | Format | |
---|---|---|---|
fulltext.pdf | 2.69 MB | Adobe PDF | View/Open |
Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.