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The notion of support provides an analogue of Stone duality, relating lattices to topological spaces. This note aims to explain in lattice theoretic terms what has been developed in the context of triangulated categories. In particular, the parallel between support via closed and open sets is addressed in terms of Hochster duality. As an application we indicate some consequences for tensor exact categories. [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]

Abstract: We characterize additive functors which are epimorphisms up to direct factors. [Copyright &y& Elsevier]

Tilting and cotilting modules are classified for the completed path algebra of a quiver of type A˜n with linear orientation. This classification problem arises naturally in the classification of cotilting modules over certain associative algebras (Pacific J. Math. 211 (2003) 41–60). The combinatorics of the collection of all tilting and cotilting modules is described in terms of Stasheff associahedra. [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]