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 …

We show that the relative Auslander-Buchweitz context on a triangulated category $\T $
coincides with the notion of co-$ t $-structure on certain triangulated subcategory of $\T …

Given a cartesian closed category $\mathcal {V} $, we introduce an internal category of
elements $\int_\mathcal {C} F $ associated to a $\mathcal {V} $-functor $ F\colon\mathcal …

We use the concept of a regular object with respect to another object in an arbitrary
category, in order to obtain the transfer of regularity in the sense of Zelmanowitz between the …

[eng] This thesis contains new results about the representability of cohomological functors
defined on a subcategory of compact objects (with respect to a fixed cardinal) of a well …

We develop a general theory of partial morphisms in additive exact categories which
extends the model theoretic notion introduced by Ziegler in the particular case of pure-exact …

Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

This thesis makes concrete some of the connections between the functor-categorical and
model-theoretic approaches to the study of modules over a ring. We show that the functor …

It is proved that, for a left hereditary ring, an arbitrary left module has a representation in the
form of the direct sum of a stable left module and indecomposable projective left modules (if …

The center Z (C) of an autonomous category C is monadic over C (if certain coends exist in
C). The notion of Hopf monad naturally arises if one tries to reconstruct the structure of Z (C) …