Embedding of categories

Abstract

In this paper we generalize the notion of exact functor to an arbitrary category and show that every small category has a full embedding into a category of all set-valued functors on some small category. The notion of exact is such that this result generalizes the author’s exact embedding of regular categories and, indeed, Mitchell’s embedding of abelian categories. An example is given of the type of diagram-chasing argument that can be given with this embedding.