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A set valued representation of the Kronecker quiver is nothing but a quiver. We apply the forgetful functor from vector spaces to sets and compare linear with set valued representations of the Kronecker quiver. [ABSTRACT FROM PUBLISHER]

We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective covers and we interpret these constructions in terms of adjoint functors. [ABSTRACT FROM AUTHOR]

Inclusion-preserving maps from modules over an Artin algebra to complete partially ordered sets are studied. This yields a filtration of the Ziegler spectrum that is indexed by all Gabriel–Roiter measures. Another application is a compactness result for the set of subcategories of finitely presented modules that are closed under submodules. [ABSTRACT FROM AUTHOR]

For a right artinian ring A we show that for every n ≥ 0 there exists a pure-injective A-module P[subn] such that the A-modules of projective dimension at most n are precisely the direct factors of A-modules having a finite filtration in products of copies of P[subn]. This is a consequence of a general description of certain contravariantly finite resolving subcategories of Mod A. It leads in addition to a one-to-one correspondence between equivalence classes of (not necessarily finitely generated) cotilting modules and resolving subcategories of Mod A which are closed under products and admit finite resolutions and special right approximations. As an application it is shown that every finitely presented partial cotilting module over an artin algebra admits a complement. [ABSTRACT FROM AUTHOR]

Abstract: The localising subcategories of the derived category of the cochains on the classifying space of a finite group are classified. They are in one to one correspondence with the subsets of the set of homogeneous prime ideals of the cohomology ring . [Copyright &y& Elsevier]