Geodesic
Universality of nonabelian cohomology
Sbornik. Mathematics, Tome 20 (1973) no. 2, pp. 283-296

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Let $T$ be the Grothendieck topology and $\mathfrak A$ a sheaf of nonabelian groups on it. We can define the one-dimensional cohomology of $\mathfrak A$ either as the Čech cohomology or as the set of $\mathfrak A$-sheaves locally isomorphic to $\mathfrak A$. In this note we put forward a construction which gives rise to a sequence of cohomological functors on the category of sheaves of nonabelian groups, which in favorable cases are shown to be universal and at the same time to coincide. Bibliography: 13 titles. 
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     author = {A. K. Tolpygo},
     title = {Universality of nonabelian cohomology},
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A. K. Tolpygo. Universality of nonabelian cohomology. Sbornik. Mathematics, Tome 20 (1973) no. 2, pp. 283-296. http://geodesic.mathdoc.fr/item/SM_1973_20_2_a5/