TY - THES
AU - Gentle, Ronald Stanley
PY - 1982
TI - A study of the sequence category
KW - Thesis/Dissertation
LA - eng
M3 - Text
AB - 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.
N2 - 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.
UR - https://open.library.ubc.ca/collections/831/items/1.0079502
ER - End of Reference