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Given a tilting object of the derived category of an abelian category of finite global dimension, we give (under suitable finiteness conditions) a bound for the global dimension of its endomorphism ring. [ABSTRACT FROM AUTHOR]

Abstract: Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective lines; this is illustrated by various applications. [Copyright &y& Elsevier]

A uniqeness result for direct sum decompositions into uniform objects is proved. The result is shown to be equivalent to the classical Krull–Remak–Schmidt Theorem for decompositions into indecomposable objects with local endomorphism rings. [Copyright &y& Elsevier]