Locally finitely presented categories with no flat objects

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.

Locally Finitely Presented Categories of Sheaves of Modules

Algebraic lattices and locally finitely presentable categories

We show that subobjects and quotients respectively of any object K in a locally finitely presentable category form an algebraic lattice. The same holds for the internal equivalence relations on K. In fact, these results turn out to be—at least in the case of subobjects—nothing but simple consequences of well known closure properties of the classes of locally finitely presentable categories and ...

Some Results on Locally Finitely Presentable Categories

We prove that any full subcategory of a locally finitely presentable (l.f.p.) category having small limits and filtered colimits preserved by the inclusion functor is itself l.f.p. Here "full" may be weakened to "full with respect to isomorphisms." Further, we characterize those left exact functors T. C —» D between small categories with finite limits for which the functor /*: LEX(D,Set) —> LEX...

Quasi-Exact Sequence and Finitely Presented Modules

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.