For a given abelian category o/, a category E is formed by considering exact sequences of o/. If one imposes the condition that a split sequence be regarded as the zero object, then the resulting sequence category E/S is shown to be abelian. The intrinsic algebraic structure of E/S is examined and related to the theory of coherent functors and functor rings. E/S is shown to be the natural setting for the study of pure and copure sequences and the theory is further developed by introducing repure sequences. The concept of pure semi-simple categories is examined in terms of E/S. Localization with respect to
pure sequences is developed, leading to results concerning the existence of algebraically compact objects. The final topic is a study of the simple sequences and their relationship
to almost split exact sequences. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/23443 |
| Date | January 1982 |
| Creators | Gentle, Ronald Stanley |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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