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Search: MSC category 18A40 ( Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) )

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1. CJM 2014 (vol 67 pp. 28)

Asadollahi, Javad; Hafezi, Rasool; Vahed, Razieh
Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor
We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left, resp. right, rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.

Keywords:derived category, Grothendieck duality, representation of quivers, reflection functor
Categories:18E30, 16G20, 18E40, 16D90, 18A40

2. CJM 2009 (vol 61 pp. 315)

Enochs, E.; Estrada, S.; Rozas, J. R. Garc\'{\i}a
Injective Representations of Infinite Quivers. Applications
In this article we study injective representations of infinite quivers. We classify the indecomposable injective representations of trees and describe Gorenstein injective and projective representations of barren trees.

Categories:16G20, 18A40

3. CJM 1999 (vol 51 pp. 294)

Enochs, Edgar E.; Herzog, Ivo
A Homotopy of Quiver Morphisms with Applications to Representations
It is shown that a morphism of quivers having a certain path lifting property has a decomposition that mimics the decomposition of maps of topological spaces into homotopy equivalences composed with fibrations. Such a decomposition enables one to describe the right adjoint of the restriction of the representation functor along a morphism of quivers having this path lifting property. These right adjoint functors are used to construct injective representations of quivers. As an application, the injective representations of the cyclic quivers are classified when the base ring is left noetherian. In particular, the indecomposable injective representations are described in terms of the injective indecomposable $R$-modules and the injective indecomposable $R[x,x^{-1}]$-modules.

Categories:18A40, 16599

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