Given a ring R, the categories of covariant additive functors (mod-R, Ab) and contravariant
additive functors ((mod-R) op, Ab) from the category mod-R of finitely presented right R …

Given a ring R, denote by mod-R the category of nitely presented right R-modules, the two
functor categories (mod-R, Ab) and ((mod-R) op, Ab) with values in the category Ab of …

Let A and B be associative rings with unit, Mod-A and Mod-B categories of unital right A-
modules and unital right B-modules respectively. For an AB-bimodule* UB, we consider two …

We show that an abelian category can be exactly, fully faithfully embedded into a module
category as the right perpendicular subcategory to a set of modules or module morphisms if …

Let A be a right coherent ring and X be a contravariantly finite subcategory of mod-A
containing projectives. In this paper, we construct a recollement of abelian categories (mod0 …

In this paper we give necessary and sufficient conditions for an additive functor u: u→ C,
from a small pre-additive category u to a Grothendieck category C, to realize C as a …

We prove the following results for the subcategories of an abelian category: 1) The full
subcategory whose objects are kernels of the maps between two covariantly finite …

For any ring R, the Auslander–Gruson–Jensen functor DA: fp (R-Mod, Ab)→(mod-R, Ab) op
is the exact functor which sends a representable functor (X,−) to the tensor functor−⊗ X. We …

The category of unital modules over a ring with identity element is characterized as a
cocomplete abelian category with a progenerator. More generally, every cocomplete abelian …

The unit element of a ring A plays an important part in classical module theory. Its existence
is equivalent to the adjointness of the free functor from the base category of abelian groups …