On pure morphisms in accessible categories

Local Cohomology and Pure Morphisms

We study a question raised by Eisenbud, Mustaţǎ, and Stillman regarding the injectivity of natural maps from Ext modules to local cohomology modules. We obtain some positive answers to this question which extend earlier results of Lyubeznik. In the process, we also prove a vanishing theorem for local cohomology modules which connects theorems previously known in the case of positive characteris...

Final coalgebras in accessible categories

We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p...

Covers in finitely accessible categories

We show that in a finitely accessible additive category every class of objects closed under direct limits and pure epimorphic images is covering. In particular, the classes of flat objects in a locally finitely presented additive category and of absolutely pure objects in a locally coherent category are covering.

On Flat Objects of Finitely Accessible Categories

Flat objects of a finitely accessible additive category C are described in terms of some objects of the associated functor category of C, called strongly flat functors. We study closure properties of the class of strongly flat functors, and we use them to deduce the known result that every object of a finitely accessible abelian category has a flat cover.

Partial Morphisms in Categories of Effective Objects