It is shown that the idempotent completion of the additive hull of the tensor product of the
residue category of the category of paths of a locally finite quiver modulo an admissible ideal …

In this paper, we prove that the lower triangular matrix category $\Lambda=\left [\begin
{smallmatrix}\mathcal {T} &0\\M&\mathcal {U}\end {smallmatrix}\right] $, where $\mathcal {T} …

The aim of this paper is to introduce a tensor structure for the quotient category of an abelian
monoidal category with biexact tensor product in order to make the canonical funtor be a …

In this thesis we study a tower of biadjunctions coming from a pivotal tensor category with a
self dual object. In order to do this, we present some relevant parts of the standard theory of …

Let R be a ring and Q be a quiver. We study the homotopy categories K (PrjQ) and K (InjQ)
consisting, respectively, of projective and injective representations of Q by R-modules. We …

We show that the idempotent completion of a triangulated category has a natural structure of
a triangulated category. The idempotent completion of the bounded derived category of an …

We define a class of morphisms between strict $\omega $-categories called discrete
Conduch {\'e} $\omega $-functors that generalize discrete Conduch {\'e} functors between 1 …

Given a thick subcategory of a triangulated category, we define a colocalisation and a
natural long exact sequence that involves the original category and its localisation and …

For a finite tensor category $\mathcal C $ and a Hopf monad $ T:\mathcal C\to\mathcal C $
satisfying certain conditions we describe exact indecomposable left $\mathcal C^ T …

We realize module functors and module natural transforms as spans of monoidal categories.
We also discuss the generalizations to algebras and modules within an arbitrary monoidal 2 …