Functors on locally finitely presented additive categories

provided that the full subcategory of finitely presented objects is skeletally small and every object is a direct limit of finitely presented objects. Our aim in this paper is to study functors which are defined on locally finitely presented categories. Roughly, most of our results are of the following form. Given a category C and some property (∗), there exists a category D satisfying (∗) and a fully faithful functor d: C → D such that any functor f: C → D ′ into a category satisfying (∗) can be extended uniquely to a functor f ∗ : D → D ′ which respects (∗) and satisfies f = f∗◦d. The following properties (∗) for a category D and combinations thereof are relevant: D has cokernels; D has kernels; D is abelian; D has direct limits. These “universal property ” type results are used to study functors between lo-cally finitely presented categories. For instance, we assign to each locally finitely