Let A be a small abelian category. For a closed subbifunctor F of Ext A 1 (−,−), Buan has
generalized the construction of Verdier's quotient category to get a relative derived category …

We clarify the relation between the subcategory D hf b (A) of homological finite objects in D b
(A) and the subcategory K b (P) of perfect complexes in D b (A), by giving two classes of …

Given a subbifunctor F of Ext1 (,), one can ask if one can generalize the construction of the
derived category to obtain a relative derived category, where one localizes with respect to F …

Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …

In a series of papers additive subbifunctors $ F $ of the bifunctor $\operatorname {Ext} _
{\Lambda}(,) $ are studied in order to establish a relative homology theory for an artin …

The notion of relative derived category with respect to a subcategory is introduced. A triangle-
equivalence, which extends a theorem of Gao and Zhang [Gorenstein derived …

Firstly we provide a technique to move torsion pairs in abelian categories via adjoint functors
and in particular through Giraud subcategories. We apply this point in order to develop a …

The notion of 𝒟-mutation pairs of subcategories in an abelian category is defined in this
article. When (𝒵, 𝒵) is a 𝒟-mutation pair in an abelian category 𝒜, the quotient category 𝒵∕ …

The notion of quotient and localization of abelian categories by dense subcategories (ie,
Serre classes) was introduced by Gabriel, and plays an important role in ring theory [6, 131 …

Using a relative version of Auslander's formula, we give a functorial approach to show that
the bounded derived category of every Artin algebra admits a categorical resolution. This, in …