Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …

Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We
may carry over various techniques from homotopy theory and homological algebra to this …

We define model structures on a triangulated category with respect to some proper classes
of triangles and give a general study of triangulated model structures. We look at the …

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 …

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 …

Let C be a triangulated category with a proper class E of triangles. Asadollahi and Salarian
introduced and studied EG projective and EG injective objects, and developed a relative …

Let C be a triangulated category. We first introduce the notion of balanced pairs in C, and
then establish the bijective correspondence between balanced pairs and proper classes ξ …

Abstract Let AA and BB be abelian categories and F: A → BF: A→ B an additive and right
exact functor which is perfect, and let (F, B)(F, B) be the left comma category. We give an …

We determine all the strongly complete projective resolutions, and all the strongly
Gorenstein projective modules, over upper triangular matrix artin algebras. In particular, we …

Let T be a triangulated category with a proper class ξ of triangles and X be a subcategory of
T. We first introduce the notion of X-resolution dimensions for a resolving subcategory of T …