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The Cohomological Dimension of a Directed Set

Published online by Cambridge University Press:  20 November 2018

Barry Mitchell
Barry Mitchell*
Affiliation:
Rutgers University New Brunswick, New Jersey
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 2 , April 1973 , pp. 233 - 238
Copyright
Copyright © Canadian Mathematical Society 1973

References

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