Geodesic
A Relationship between Left Exact and Representable Functors
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 374-380

Voir la notice de l'article provenant de la source Cambridge University Press

Our aim in this paper is to demonstrate a relationship between left exact and representable functors. More precisely, in the functor category whose objects are the additive functors from the dual of an abelian category A to the category of abelian groups and whose morphisms are the natural transformations between them, the left exact functors can be characterized as those equivalent to a direct limit of representable functors taken over a directed class. The proof will proceed in the following manner. Lambek [3] and Ulmer [7] have shown that any functor T in can be expressed as a direct limit of representable functors taken over a comma category. When T is left exact, it is easily observed that this comma category is a filtered category. When T is left exact, it is easily observed that this comma category is a filtered category. 
Stauffer, H. B. A Relationship between Left Exact and Representable Functors. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 374-380. doi: 10.4153/CJM-1971-038-2
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