Recollements of Quiver Representations Induced by Evaluation Functors

Let [Formula: see text] be an arbitrary acyclic quiver and [Formula: see text] an abelian category satisfying [Formula: see text] and [Formula: see text]. Let [Formula: see text] be the category of [Formula: see text]-valued representations of [Formula: see text] and [Formula: see text] its full subcategory consisting of representations with 0 at vertex [Formula: see text]. We construct a recollement of [Formula: see text] by [Formula: see text] and [Formula: see text]. If in addition, [Formula: see text] has enough projective and injective objects, and satisfies [Formula: see text] and [Formula: see text], then this recollement can be lifted to the derived levels. In the case that [Formula: see text] is finite and [Formula: see text] is the module category [Formula: see text] over some finite dimensional algebra [Formula: see text], we give several direct applications concerning the relationship between homological properties of [Formula: see text] and [Formula: see text]. In particular, we find that the Cartan determinant conjecture always holds true for [Formula: see text] with [Formula: see text] an even number.