The Cohomological Dimension of a Directed Set
- 1 April 1973
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 25 (2) , 233-238
- https://doi.org/10.4153/cjm-1973-023-0
Abstract
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.Keywords
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