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On factorization structures, denseness, separation and relatively compact objects

We define morphism (E, M)-structures in an abstract category, develop their basic properties and present some examples. We also consider the existence of such factorization structures, and find conditions under
which they can be extended to factorization structures for certain classes of sources. There is a Galois correspondence between the collection of all subclasses of X-morphisms and the collection of all subclasses of
X-objects. A-epimorphisms diagonalize over A-regular morphisms. Given an (E, M)-factorization structure on a finitely complete category, E-separated objects are those for which diagonal morphisms lie in M. Other characterizations of E-separated objects are given. We give a bijective correspondence between the class of all (E, M)factorization structures with M contained in the class of all X-embeddings and the class of all strong limit operators. We study M-preserving morphisms, M-perfect morphisms and M-compact objects in a morphism (E, M)-hereditary construct, and prove some of their properties which are analogous to the topological ones. / Mathematical Sciences / M. Sc. (Mathematics)

Identiferoai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/16050
Date04 1900
CreatorsSiweya, Hlengani James
ContributorsAlderton, Ian William, 1952-
Source SetsSouth African National ETD Portal
LanguageEnglish
Detected LanguageEnglish
TypeDissertation
Format1 online resource (ix, 137 leaves)

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