A study of the sequence category

• Main Author: Gentle, Ronald Stanley
• Language: English
• Published: 2010
• Subjects: Sequences (Mathematics); Rings (Algebra); Abelian categories
• Online Access: http://hdl.handle.net/2429/23443

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