A locally coherent exact category is a finitely accessible additive category endowed with an
exact structure in which the admissible short exact sequences are the directed colimits of the …

Let $\kappa $ be a regular cardinal, $\lambda<\kappa $ be a smaller infinite cardinal, and
$\mathsf K $ be a $\kappa $-accessible category where colimits of $\lambda $-indexed …

A general principle suggests that" anything flat is a directed colimit of countably presentable
flats". In this paper, we consider resolutions and coresolutions of modules over a countably …

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 …

Contraherent cosheaves are module objects over algebraic varieties defined by gluing
using the colocalization functors. Contraherent cosheaves are designed to be used for …

Abstract Let\((\mathcal {G},\otimes)\) be any closed symmetric monoidal Grothendieck
category. We show that K-flat covers exist universally in the category of chain complexes …

For any CDG-ring $ B^\bullet=(B^*, d, h) $, we show that the homotopy category of graded-
projective (left) CDG-modules over $ B^\bullet $ is equivalent to the quotient category of the …

For any commutative ring $ R $, we show that the categories of $ R $-coalgebras and
cocommutative $ R $-coalgebras are locally $\aleph_1 $-presentable, while the categories …

This paper is a follow-up to arXiv: 2212.09639. We consider an algebraic setting of
comodules over a coring, corresponding to a (noncommutative) algebraic geometry setting …