Given any additive category C with split idempotents, pseudokernels and pseudocokernels,
we show that a subcategory B is coreflective if, and only if, it is precovering, closed under …

We generalize to exact categories some new perspectives on projectivity, which allow us to
unify a series of recent concepts from module categories or abelian categories and to obtain …

Given a full subcategory [Fscr] of a category [Ascr], the existence of left [Fscr]-approximations
(or [Fscr]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that …

We show that an abelian category can be exactly, fully faithfully embedded into a module
category as the right perpendicular subcategory to a set of modules or module morphisms if …

We investigate how to characterize subcategories of abelian categories in terms of intrinsic
axioms. In particular, we find axioms which characterize generating cogenerating functorially …

One of the earliest theorems in category theory stated that an abelian category could be
represented faithfully by exact functors into the category Ab of abelian groups [Freyd …

In an abelian category $\mathscr {A} $ with small ${\rm Ext} $ groups, we show that there
exists a one-to-one correspondence between any two of the following: balanced pairs …

Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory
generated by X. We give a one-to-one correspondence between simple semibricks and …

We consider trivial and central extensions, in the sense of G. Janelidze and GM Kelly, which
are defined with respect to an adjunction between a Barr-exact category C and a Birkhoff …

We prove that some subquotient categories of exact categories are abelian. This
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …