… theorems, but illustrate the principle that important statements about functors viewed as
functors may follow from statements about functors viewed as objects in an abelian category. …

… These categories will be the main object of this article. … We show first that T is closed
with respect to subobjects. Thus let i : N -> M be a monomorphism in mod(A) with …

… objects in abelian categories, which is an extension of the definition given by Angeleri-Coehlo
[Citation3] for the setting of the abelian category … This definition of tilting (cotilting) object …

… abelian category is noetherian if all objects of this category are noetherian, that an abelian
category is … The theory is analogous in every respect to the theory of semi-simple modules [4]. …

… abelian categories following Grothendieck [12]. We then characterize module categories
among abelian categories. … An additive category is a Z-category A which has a zero object 0 (ie …

… Abelian category in the sense below such that for any object … In this case we denote the object
Coker a by B/A. We call the … F are each complete with respect to the orthogonality relation (…

… abelian category. To define stability in a category A we need first a preorder on the objects …
We will say that a preorder on A is given when we can compare nonzero objects of A that for A…

… abelian R-category H with tilting object is derived equivalent to a noetherian hereditary abelian
category… , and when tilting with respect to this torsion pair, we obtain a hereditary abelian …

… This means that the abelian category C is the Gabriel quotient of B with respect to A . In …
objects in a recollement of abelian categories. Recall that an object X in an abelian category A is …

… The spectrum, Spec<A, of the category A is the preordered set of equivalence (with respect
… is extended to any abelian category A with the property (sup) as follows. For any object V of A…