Geodesic
On the homological classification of small categories
Sbornik. Mathematics, Tome 22 (1974) no. 3, pp. 386-409 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {S. V. Polin},
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S. V. Polin. On the homological classification of small categories. Sbornik. Mathematics, Tome 22 (1974) no. 3, pp. 386-409. http://geodesic.mathdoc.fr/item/SM_1974_22_3_a3/

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[2] M. S. Tsalenko, E. G. Shulgeifer, Lektsii po teorii kategorii, izd-vo MGU, Moskva, 1970 | MR

[3] E. G. Shulgeifer, “Kategoriya funktorov nad mnogoobraziem universalnykh algebr”, Izv. AN SSSR, seriya matem., 36 (1972), 386–400

[4] M. S. Tsalenko, “K osnovam teorii kategorii”, Uspekhi matem. nauk, XV:6 (96) (1960), 53–58

[5] P. Gabriel, M. Tsisman, Kategorii chastnykh i teoriya gomotopii, izd-vo «Mir», Moskva, 1971 | MR

[6] A. Klifford, G. Preston, Algebraicheskaya teoriya polugrupp, t. I, izd-vo «Mir», Moskva, 1972