Browsing by Subject "Quiver representation"

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    Balanced pairs, cotorsion triplets and quiver representations
    (Cambridge University Press, 2019-08-13) Estrada, Sergio; Pérez, Marco A.; Zhu, Haiyan; Matemáticas
    Balanced pairs appear naturally in the realm of relative homological algebra associated with the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural source of such pairs. In this paper, we study the connection between balanced pairs and cotorsion triplets by using recent quiver representation techniques. In doing so, we find a new characterization of abelian categories that have enough projectives and injectives in terms of the existence of complete hereditary cotorsion triplets. We also provide a short proof of the lack of balance for derived functors of Hom computed using flat resolutions, which extends the one given by Enochs in the commutative case.