3 papers
math.AC2026
Resolutions as directed colimits
Leonid Positselski
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 c…
math.CT2026
On pure monomorphisms and pure epimorphisms in accessible categories
Leonid Positselski
In all -accessible additive categories, -pure monomorphisms and -pure epimorphisms are well-behaved, as shown in our previous paper arXiv:2311.02418. This is known to b…
math.RA2025
The categories of corings and coalgebras over a ring are locally countably presentable
Leonid Positselski
For any commutative ring , we show that the categories of -coalgebras and cocommutative -coalgebras are locally -presentable, while the categories of -flat $R…