Quasireflections and quasifactorizations

Simple item page
dc.contributor.advisorBrümmer, Guillaume C Len_ZA
dc.contributor.advisorBargenda, Hubertus Wen_ZA
dc.contributor.authorHenning, Peteren_ZA
dc.date.accessioned2016-03-17T12:37:24Z
dc.date.available2016-03-17T12:37:24Z
dc.date.issued1996en_ZA
dc.descriptionBibliography: pages 37-38.en_ZA
dc.description.abstractThe study of reflections in abstract category theory is widespread, and has often been used to study the concrete notion of "completion of an object" that occurs in. many fields of Mathematics, such as the Cech-Stone compactification of a Tychonoff space ([Cech 37]) or the completion of a uniform space ([Weil 38]). More recent work relating reflections to completions was published by Brummer and Giuli [Brummer Giuli 92], and in this thesis many of their ideas are extended to the more general setting of quasireflections (Bargenda 94]. In particular, one would like to view the well-known concept of an injective hull as a "completion", and this can be accomplished via a Galois correspondence between such hulls on one hand, and quasireflections on the other. Thus the theory of completion of objects can be extended to include many widely studied and significant examples, the most paradigmatic of which is the Mac Neille completion of a partially ordered set [Mac Neille 37]. These ideas are presented in chapters 1 and 2 of the present thesis. Further, the widely accepted characterization of factorization structures for sources in terms of certain colimits (pushouts and cointersections) was successfully extended to a characterization of factorization structures relative to a subcategory in the PhD thesis of Vaclav Vajner ([Vajner 94]). In chapter 3 of this thesis, the characterization is further generalized to include quasifactorization structures relative to a subcategory. This result relates to the results of chapters 1 and 2 via an important result of Bargenda's, which proves a Galois correspondence between quasireflective subcategories and relative quasifactorization structures (proposition 3.7).en_ZA
dc.identifier.apacitationHenning, P. (1996). <i>Quasireflections and quasifactorizations</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17937en_ZA
dc.identifier.chicagocitationHenning, Peter. <i>"Quasireflections and quasifactorizations."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1996. http://hdl.handle.net/11427/17937en_ZA
dc.identifier.citationHenning, P. 1996. Quasireflections and quasifactorizations. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Henning, Peter AB - The study of reflections in abstract category theory is widespread, and has often been used to study the concrete notion of "completion of an object" that occurs in. many fields of Mathematics, such as the Cech-Stone compactification of a Tychonoff space ([Cech 37]) or the completion of a uniform space ([Weil 38]). More recent work relating reflections to completions was published by Brummer and Giuli [Brummer Giuli 92], and in this thesis many of their ideas are extended to the more general setting of quasireflections (Bargenda 94]. In particular, one would like to view the well-known concept of an injective hull as a "completion", and this can be accomplished via a Galois correspondence between such hulls on one hand, and quasireflections on the other. Thus the theory of completion of objects can be extended to include many widely studied and significant examples, the most paradigmatic of which is the Mac Neille completion of a partially ordered set [Mac Neille 37]. These ideas are presented in chapters 1 and 2 of the present thesis. Further, the widely accepted characterization of factorization structures for sources in terms of certain colimits (pushouts and cointersections) was successfully extended to a characterization of factorization structures relative to a subcategory in the PhD thesis of Vaclav Vajner ([Vajner 94]). In chapter 3 of this thesis, the characterization is further generalized to include quasifactorization structures relative to a subcategory. This result relates to the results of chapters 1 and 2 via an important result of Bargenda's, which proves a Galois correspondence between quasireflective subcategories and relative quasifactorization structures (proposition 3.7). DA - 1996 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1996 T1 - Quasireflections and quasifactorizations TI - Quasireflections and quasifactorizations UR - http://hdl.handle.net/11427/17937 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/17937
dc.identifier.vancouvercitationHenning P. Quasireflections and quasifactorizations. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1996 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17937en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.subject.otherTopologyen_ZA
dc.titleQuasireflections and quasifactorizationsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
thesis_sci_1996_henning_peter.pdf
Size:
1020.09 KB
Format:
Adobe Portable Document Format
Description:
Download
Collections
Masters