Let k be a field. We show that locally presentable, k-linear categories CC dualizable in the
sense that the identity functor can be recovered as ∐ _i x_i ⊗ f_i∐ ixi⊗ fi for objects x_i ∈ C …

We prove a derived version of the Gabriel–Popescu theorem in the framework of dg-
categories and t-structures. This exhibits any pretriangulated dg-category with a suitable t …

The concept of an abelian DG-category, introduced by the first-named author in Positselski
(Exact DG-categories and fully faithful triangulated inclusion functors. arXiv: 2110.08237 …

For a commutative ring $ A $, we have the category of (bounded-below) chain complexes of
$ A $-modules $ Ch_ {+}(A\mymod) $, a closed symmetric monoidal category with a …

Given a commutative ring A there are different approaches to understand its structure; one is
consider ideals and their arithmetic (multiplicative theory), and another one is to consider …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

Let RR be a ring with identity. Inspired by recent work in Emmanouil, Preprint, 2021, we
show that the derived category of RR is equivalent to the chain homotopy category of all K …

We classify bounded t-structures on the category of perfect complexes over a commutative,
Noetherian ring of finite Krull dimension, extending a result of Alonso Tarrío, Jeremías López …

Let $ A $ be a commutative unital ring. We prove the MGM equivalence and the Greenless-
May duality in the category of chain complexes of $ A $-modules. This extends the above …

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 …