In this paper, we investigate the homological properties of the functor categories (mod− R,
Ab) and ((mod− R) op, Ab). Some new homological dimensions in these functor categories …

Let R be a commutative Noetherian ring, a an ideal of R, and M, N two finitely generated R-
modules. Let t be a non-negative integer. It is shown that for any finitely generated R-module …

Let T be a right exact functor from an abelian category B into another abelian category A.
Then there exists an abelian category, named comma category and denoted by (T↓ A). In …

We introduce and discuss the notion of a naturally full functor. The definition is similar to the
definition of a separable functor; a naturally full functor is a functorial version of a full functor …

Tensor products of functors over the set category are studied in this work. The concept of a
plane functor is defined and a criterion under which a functor is planar is given, by means of …

In this paper, we give some characterizations of FP-grinjective R-modules and graded right
R-modules of FP-gr-injective dimension at most n. We study the existence of FP-gr-injective …

In this paper, we extend the notion of C-injective module to that of C-FP-injective module,
where S CR is a semidualizing bimodule over associative rings. We first obtain a result on …

Abstract Let\({\cal C}=({\cal C},\mathbb {E},\mathfrak {s})\) be an extriangulated category. In
this paper, we give the notion of ideal balanced pairs in\({\cal C}\) and some equivalent …

In this paper, we extend the notions of n-FP-injective and n-flat modules to that of complexes
which we call n-FP-injective and n-flat complexes, respectively and we show that the class of …