We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

A triangulated category is an additive category C equipped with an automorphism Σ: C→ C,
called the suspension functor, and a class of diagrams in C of the form A→ B→ C→ ΣA …

We prove that, for any n≥ 2, the classes of FP n-injective modules and of FP n-flat modules
are both covering and preenveloping over any ring R. This includes the case of FP∞ …

The object of this article is to determine when a commutative Artin local ring A is the
homomorphic image ofa Gorenstein ring t F in such a way that the kernel of the …

For a self-orthogonal module T, the relation between the quotient triangulated category D b
(A)/K b (add T) and the stable category of the Frobenius category of T-Cohen-Macaulay …

Projectively coresolved Gorenstein flat modules were introduced recently by Saroch and
Stovicek and were shown to be Gorenstein projective. While the relation between …

1. Preliminaries. In this note we introduce a new tensor product functor in the category of
complexes. We show that this tensor product is left adjoint to the Hom functor properly …

K-flatness for unbounded complexes of modules over a ring R was introduced by
Spaltenstein [27], as an analogue of the classical notion of flatness for modules. In this …

Let A and B be two rings, M be a left B, right A bimodule and be the formal triangular matrix
ring. It is known that the category of right T-modules is equivalent to the category Ω of triples …

We define and study a notion of Gorenstein projective dimension for complexes of left
modules over associative rings. For complexes of finite Gorenstein projective dimension we …