It is common to encounter symmetric monoidal categories $\mathcal {C} $ for which every
object is equipped with an algebraic structure, in a way that is compatible with the monoidal …

The concept of an abelian DG-category, introduced by the first-named author in arXiv:
2110.08237, unites the notions of abelian categories and (curved) DG-modules in a …

Recently a notion of support and a construction of local cohomology functors for [TR5]
compactly generated triangulated categories were introduced and studied by Benson …

We define model structures on exact categories, which we call exact model structures. We
look at the relationship between these model structures and cotorsion pairs on the exact …

We present some results on (co) limits of diagrams in $\infty $-categories, as well as those in
$(n, 1) $-categories. In particular, we deduce a way to reshape colimit diagrams into …

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 …

Let R be a ring with identity and C (R) denote the category of complexes of R-modules. In
this paper we study the homotopy categories arising from projective (resp. injective) …

Duality properties are studied for a Gorenstein algebra that is finite and projective over its
center. Using the homotopy category of injective modules, it is proved that there is a local …

For a finite acyclic quiver Q, an ideal I of a path algebra kQ generated by monomial relations,
and a finite-dimensional k-algebra A, we introduce the separated monic representations of a …

Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M 0 & B\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. Given two complete hereditary …