Geodesic
The Cohomological Dimension of a Directed Set
Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 233-238

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a ring with identity, and let C be a small, nonempty category. We denote the category of right R-modules by AbR and the category of contravariant functors C → AbR by AbRC*. The limit functor is left exact, and its kth right derived functor is denoted by colimk . The R-cohomological dimension of C is defined by If there is a unitary ring homomorphism R→S, then it is not difficult to show that cdsC ≦ cdRC. 
Mitchell, Barry. The Cohomological Dimension of a Directed Set. Canadian journal of mathematics, Tome 25 (1973) no. 2, pp. 233-238. doi: 10.4153/CJM-1973-023-0
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