Quasireflections and quasifactorizations

 

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dc.contributor.advisor Brümmer, Guillaume C L en_ZA
dc.contributor.advisor Bargenda, Hubertus W en_ZA
dc.contributor.author Henning, Peter en_ZA
dc.date.accessioned 2016-03-17T12:37:24Z
dc.date.available 2016-03-17T12:37:24Z
dc.date.issued 1996 en_ZA
dc.identifier.citation Henning, P. 1996. Quasireflections and quasifactorizations. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/17937
dc.description Bibliography: pages 37-38. en_ZA
dc.description.abstract 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). en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics en_ZA
dc.subject.other Topology en_ZA
dc.title Quasireflections and quasifactorizations en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Henning, 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/11427/17937 en_ZA
dc.identifier.chicagocitation Henning, 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/11427/17937 en_ZA
dc.identifier.vancouvercitation Henning 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/11427/17937 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


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