On the homological classification of small categories

Necessary and sufficient conditions on a small category $\mathfrak d$ are given in order that every functor from $\mathfrak d$ to the category $\mathfrak S$ of all sets be a projective object in the category $\mathfrak F(\mathfrak d,\mathfrak S)$, and also in order that every functor from $\mathfrak d$ to the category $\mathfrak S_n$ of nonvoid sets be an injective object in the category $\mathfrak F(\mathfrak d,\mathfrak S_n)$.
Bibliography: 6 titles.