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Cohomologies and extensions of categories. (Cohomologies et extensions de catégories.) (French) Zbl 0823.18007

In a previous work [On the cohomology of categories, Rend. Mat., VI. Ser. 7, 169-192 (1974; Zbl 0361.18012)], the author has defined extensions of categories in order to describe an abelian, and with functorial coefficients, cohomology of small categories in dimension 2.
This notion provides also an interpretation, in terms of extensions, of not necessary abelian, and with not necessary functorial coefficients, cohomologies. Furthermore, the links with fibered categories permit to extend the notion of extensions and the cohomologies so described. In this framework, the notion of coefficients, which often define the cohomologies, is also naturally visited.

MSC:

18G50 Nonabelian homological algebra (category-theoretic aspects)
18D30 Fibered categories
18A22 Special properties of functors (faithful, full, etc.)
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
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