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Derived functors are compatible with shifts

Lemma 13.14.5. Assumptions and notation as in Situation 13.14.1. Let $X$ be an object of $\mathcal{D}$ and $n \in \mathbf{Z}$.

  1. $RF$ is defined at $X$ if and only if it is defined at $X[n]$. In this case there is a canonical isomorphism $RF(X)[n]= RF(X[n])$ between values.

  2. $LF$ is defined at $X$ if and only if it is defined at $X[n]$. In this case there is a canonical isomorphism $LF(X)[n] \to LF(X[n])$ between values.

Proof. Omitted. $\square$

Comments (1)

Comment #2113 by Matthew Emerton on

Suggested slogan: Derived functors are compatible with shifts

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  • 4 comment(s) on Section 13.14: Derived functors in general

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