We present the concept of cotorsion pairs cut along subcategories of an abelian category.
This provides a generalization of complete cotorsion pairs, and represents a general …

Consider the obvious functor from the unbounded derived category of all finitely generated
modules over a left noetherian ring R to the unbounded derived category of all modules. We …

We define and study opfibrations of V-enriched categories when V is an extensive monoidal
category whose unit is terminal and connected. This includes sets, simplicial sets …

We show that, over an arbitrary commutative ring, the localizations of the categories of dg
categories, of unital and of strictly unital A∞ categories with respect to the corresponding …

Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …

Abridged abstract: In this article we develop formal category theory within augmented virtual
double categories. Notably we formalise the notions of Kan extension and Yoneda …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …

Motivated by the classical structure of Tate cohomology, we develop and study a Tate
cohomology theory in a triangulated category C. Let E be a proper class of triangles. By …