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STABLE CATEGORIES OF ABELIAN CATEGORIES

By ΑΠΟΣΤΟΛΟΣ ΜΠΕΛΗΓΙΑΝΝΗΣ

Abstract

THIS DISSERTATION CONSISTS OF TWO COHERENT PARTS. IN THE FIRST PART (CHAPTERS I,II,III) WE INTRODUCE THE CONCEPT OF THE CLEFT EXTENSION OF AN ABELIAN CATEGORY AND WE STUDY THE MAIN PROPERTIES, EMPHASIZING THE RELATIVE HOMOLOGICALBEHAVIOUR, OF A CLEFT EXTENSION. WE GIVE APPLICATION TO THE CLEFT EXTENSION OF RINGS. IN THE SECOND PART (CHAPTER IV) WE STUDY THE RELATIVE HOMOLOGY OF APARTICULAR CLASS OF CLEFT EXTENSIONS OF ADDITIVE CATEGORIES. WE CONCENTRATE OUR STUDY TO THE STABLE BEHAVIOUR OF ADDITIVE CATEGORIES WITH RESPECT THEIRHOMOLOGICALLY FINITE SUBCATEGORIES. WE GIVE APPLICATIONS TO ABELIAN AND TRIANGULATED CATEGORIES.

Topics: ABELIAN CATEGORIES, CLEFT EXTENSIONS, FINITELY PRESENTED OBJECTS, RELATIVE HOMOLOGY, STABLE CATEGORIES, TRIANGULATED CATEGORIES, ΑΒΕΛΙΑΝΕΣ ΚΑΤΗΓΟΡΙΕΣ, ΕΥΣΤΑΘΕΙΣ ΚΑΤΗΓΟΡΙΕΣ, ΠΕΠΕΡΑΣΜΕΝΑ ΠΑΡΑΣΤΑΣΙΜΑ ΑΝΤΙΚΕΙΜΕΝΑ, ΣΦΗΝΟΕΙΔΕΙΣ ΕΠΕΚΤΑΣΕΙΣ, ΣΧΕΤΙΚΗ ΟΜΟΛΟΓΙΑ, ΤΡΙΓΩΝΙΣΜΕΝΕΣ ΚΑΤΗΓΟΡΙΕΣ
Publisher: University of Ioannina
Year: 1995
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