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 …

Contramodules are module-like algebraic structures endowed with infinite summation (or,
occasionally, integration) operations satisfying natural axioms. Introduced originally by …

For four wide classes of topological rings R, we show that all flat left R-contramodules have
projective covers if and only if all flat left R-contramodules are projective if and only if all left …

Let $ R $ be a ring and $\mathsf S $ be a class of strongly finitely presented (FP ${} _\infty $)
$ R $-modules closed under extensions, direct summands, and syzygies. Let $(\mathsf …

Abstract Extending the Wedderburn–Artin theory of (classically) semisimple associative
rings to the realm of topological rings with right linear topology, we show that the abelian …

Enochs' conjecture asserts that each covering class of modules (over any fixed ring) has to
be closed under direct limits. Although various special cases of the conjecture have been …

Let C be a class of modules and L= lim→ C the class of all direct limits of modules from C.
The class L is well understood when C consists of finitely presented modules: L then enjoys …

We present applications of contramodule techniques to the Enochs conjecture about covers
and direct limits, both in the categorical tilting context and beyond. In the n-tilting–cotilting …

Enochs' conjecture asserts that each covering class of modules (over any ring) has to be
closed under direct limits. Although various special cases of the conjecture have been …

We study and relate categories of modules, comodules and contramodules over a
representation of a small category taking values in (co) algebras, in a manner similar to …